Take it to a local machine shop. They should have the tools and know how. If you mess up, well...

Good call.
I think the hood ornament is proper but the wheels maybe mixed. They made a rim like that 31-32 but had a different cap. This cap looks larger like the one for the wire wheels. The lack of chrome on the grill shell is the tell tale for the '31-on. Earlier and later had chrome.
I couldn't zoom on the cap but what little I saw didn't look right.
You can check with the Auburn museum.
www.automobilemuseum.org/

Since your dealing with old lacquer, I'd not recommend to clear over with modern clears. Might as well use paint if you're going that route. Prep is the same.
Original lacquer tends to "dry out", crack, and chip as part of its aging. Applying new clear lacquer will shrink the surface only and could cause more lifting issues. You have to sand it down for good adhesion and that takes away from the patena. Water based clear has to heat cure and that'll mess up the other parts. Plus in prep you might sand through and make it look worse.
I'd recommend hand rubbing(compound) over color sanding or if you're good with an oscillating machine. I start with polishing compound and go to rubbing only, if needed, to match the gloss. Old paint is more pliable this way. There's some more tricks o' trade so consider consulting a detail shop. Depending on the paint condition, you'll likely not restore full luster with color sanding anyway and could go through. Color sanding is good for leveling newer paint or paint that has surface imperfections and you want higher gloss or fixing scratches, etc.
Since you say the top half paint is "better", in order to keep the iron cancer out, consider to spot spray and blend the bottom.
Clean it good and leave it alone then twice yearly coats of a good grade of carnuba wax will seal the paint and metal. Chrome will clean up fairly good and wax it also.
There's a mil spec. "silicone" spray the govt uses for aircraft that preserves rubber when it goes to the bone yard. We used to use it for detailing but I'm not sure if it's around anymore. I'll have research that one.
Well, I'm not getting my undercoat paint done sitting here.

Reminder: the key word about flushes is change "filter".
Alot of the earlier motors had NO oil filter, as my '49 288. Those that did had something not much better than a gravity filter treating a slip stream of the crankcase flow.
So deposits accumulate in the old motors depending how frequent oil is changed. Some of the earlier oils also had problems with parafins(wax), that caused even more sludge.
Detergent oils didn't come until awhile after the war.
It's a fascinating history to study lubrication from the guy in overalls with the big oil can to modern systems. It's a subject unto itself. It's still evolving and the experts disagree on what best. I've seen my boat trailer bearing lube systems change 360 in the last 25 years from grease to oil back to grease. i.e. nothing works well int hat service.
I did some work in oil recovery about 40 years ago, and it's changed alot but the elements remain the same, search for that magic fluid that prevents wear, mostly a figment of the marketing department imagination and snake oil salesmen talk. Also, oversaw some grease and solid lubricant manufacture, but did little there. We used lubricators quite a bit for high pressure/speed seals.

The radiator support does unbolt as one piece but is not easy to remove without taking the front clip off. You can see in the picture alot of sheet metal screws and a couple bolts. It's around 10-12 fasteners.
The hoop is spot welded to the uprights on each side in the crease underside. You can see then in the picture. I assume he just completely drilled them out. You can use a spot weld cutter then weld back as well. It'll be closer to original that way than bolts. If you weld on car just be sure to cover everything to protect the paint, chrome, etc.
ps:Site needs to organize some of this info, because I went thru the same discussion last year and this info should be all in one spot "pulling engines" to not reinvent the wheel each time.

If most likely stuck VR doesn't solve it;
wiring looks a bit toasted, may need to check for insulation losses. Short is best way I know to pull full amps.
If the gen is gone(brushes) that's another one to check. When it cuts to gen, it may not be putting out and draws battery further. When gen is off, it's OK. Eventually the battery dies. Lights will be dim.
I like a installed volt meter in my generator cars so you can better determine what's going on.
It appears the "ammeter" is functioning but there's some other that need checked as well to rule out its not a gauge issue.

There was a good article in the Cad-Lasalle club monthly a month ago about all the sources of losing hubcaps, including the radial vs bias myth, rim stock differences, etc. Unfortunately it's copyrighted.
My own take is, as you said, you hit a bad patch of road and whamo. Avoidance: #1 thing to do if you like your hubcaps!
That's what I remember how hubcaps flew off, because we used to hunt for them along the roads as kids and we had real bad roads after winter. They just came off back then and from all make cars.
The second best thing you can do is check your shock absorbers, springs, and suspension parts. They're what "cushions" those blows and limits/dampens travel and vibration when you hit a hole. Too stiff, mushy, or loose isn't good. If it "shudders" when you hit something it's not right.
I lost two before I ever got my car! They were in the trunk, but didn't show up on arrival??? I can also attest that 4 of 5 clips on the rim won't hold one on a decent road. I lost one in my own neighborhood test driving. It disappeared rapidly(kids or maybe some dog used it for a dish???) before I recognized it was gone, so you're lucky to have seen yours.
Perhaps a request how to fix damaged hubcaps is in order? These have a SS skin and a steel inner if I recall.
Some people use different sorts of techniques to keep them on as well, like strip magnets, velcro, wires, putty, etc. but have no recommendations there.
You can get new clips as well. I'd not trust oldies to have much spring and bending won't improve temper. According to the parts list, there were clip and non-clip rims vs the correct hubcap P/N. It's not real clear what cap goes with what P/N, but you can peruse the photos/sales info. My deluxe does not have the red center for instance.

1 If you have some seat back material you can match. Take from the inside or seams where not faded.
2 You can contact the PAC roster keeper for those years.
3 I think there's a list on here of the trim codes and what they were. But it doesn't cover everything. I extensively searched and was unable to find a cross reference anywhere, to vendors materials, etc. even the museums, so don't bother with that search.
4 Perhaps a custom restorer shop may know or think they know but they usually want your business. LeBaron Bonney specializes in NOS GM, but some were the same. I could not match with them. They do make interiors.
5 I had alot of luck finding correct from "SMS Auto fabric" and some others.
6 Sam was in the process of making some front rubber for a few cars this summer, but don't know where he stands on that.
I'm going a bit custom, so I just bought some logo mats that can be stitched into regular auto carpet.

It's just one of those things that isn't well documented in this era or lost, but I still believe the info exists but it's not retrivable at present.

Easy way isn't always the best way. The whole concept is suspect. Sounds like you're not rebuilding but fixing some valve train damage in the car and suspect it was caused by lack of lubrication. You want to do something so it doesn't reoccur, but aren't sure what.
First, I would think one would clean before attempting repairs, so you could check for damaged components, not after repair?
Second, a proper "rebuild" would require complete disassembly and have all cleaned, trued, checked, etc.
Third, I'm not up on 40s, so gurus chime in, but I thought these were solid not hydraulic lifters.
Fourth,to do any significant cleaning of the passages would require high pressure and flow and you only have at best the oil pump to do it and it's cranking slowly. Proper type flow won't occur at low (turnover) speed. For that reasons, they make a drill adapter down the distributor, where appropriate, to turn over newly rebuilt motors to get the oil flowing properly.
Fifth, you risk more damage by clogging the oil pump and may not get clean blocked passages anyway, no matter what fluid you use at that speed.
Simple fixes. There's always the old run a wire through the passages or blow out with an air gun, if you can get to them. Or take something like Blaster or WD 40 with a nozzle tube and spray to see if it passes through each one.
What plugs the passages is similar to the sludge that settles out in the pan, a combination of metallic fines from wear and thermally degraded oil and additives or "char". These are discrete sub micron particles that became insoluble in the oil and settle out but can stick together. The diesel fuel may soft the carbon deposits but won't touch the metallics. A diesel injector cleaner may be more appropriate but those rely on a warm, not cold, functioning motor. As old school, I prefer to soak parts in kerosene (or carb cleaner), repeat until fluid comes out clean and then inspect/clean manually. There are chlorinated materials that will easily "degrease" this but are not recommended for what you propose as they'll do too good a job and damage the seal/bearings from lack of lube. Mostly they've gone to hot aqueous type block cleaners, detergents and enzymes, now for environmental reasons as well. So to use that requires further tear down and possibly a drying oven.

M I C,
K E Y...
M-O-U-S-E!