Sounds like it rusted off, which is common from the manifold heat. They can be repaired - carefully. Having done it on the car, I'd suggest to take the manifold off. Or use an electric or manual choke.

Swirl marks are not necessary in any surface. They are scratches or smeared surface material that wasn't cleaned off.
A lot of people back then didn't know how to properly care for their finishes, (mythology) so it can be an "authenticity" item for a survivor but not necessary in repaint, restoration, or regular care.
Properly done, the paint surface is stepwise cleaned and leveled, then sealed with a wax or polymer and buffed to gloss to prevent UV, water, and oxidation damage that occurs through natural outdoor aging. A clean surface properly treated gives that mile deep wet shine. Must remove all water spots!
Some of the newer polishes/glazes haze and have to be wiped or reapplied frequently to maintain luster.
{I've been detailing for 50 years and sure others here have as much or more. It's got a lot easier with the new finishes, compounds, and waxes. I dare you to hand rub a "new" or "faded" lacquer or enamel job and hand rub it to gloss with "original" hard simoniz, ex machine. Some people didn't want machine use because they thought swirls marks were inevitable with them. I did my share at $20 a pop back in the day when $20 was good pocket money. I wouldn't trade my new orbital buffer w/ sponge pads and some of the Meguiar's or Mothers cleaners and polishes out there.} The Geek guys are good. It's better to keep a light finish maintenance effort than let it go and have to take it back from "scratch".

"Hot" or "higher" is forcing more heat out, so in effect it's a good thing, up until it effects the lubrication and other aspects like fuel delivery, etc. So if it's just a few degrees higher in the hot weather, idling, I'd not worry unless you want a perfect running original. The seven psi cap will take around 215-220F. It's counter intuitive but DO NOT use a lower temp. thermostat.
The real issue is are one or more local areas "really hot" due to restrictions. A thermal scan may indicate that. Nothing less than "boiling out" the block would accomplish "factory" heat transfer performance.
If you aggressively try to clean the water jacket, you open up the possibility of leaks, etc. I'd just repeat the drain and system flush a few more times and take what I got. The issue is not to transfer junk from the motor to the radiator where the passages are smaller, so disconnect the hoses/separate. These motors are hard to flush and reversing the flow can't hurt. I stuck a hose nozzle down the thermostat hole as Owen suggests and reverse flushed mine.
Is the hood/bonnet up during this time? It's designed to take air in the front through the radiator and opening the hood can short circuit the fan.
If it doesn't cool down after it's moving then I'd go further with disassembly. A fan shroud might help increasing air flow at idle. They didn't come about until later. These motors turn rather slow at idle compared to most so a low speed open fan is not an effective air mover to begin with. Is it idling too fast? After I got it running, my 2365 would idle in the drive at 400 rpm almost indefinitely and not heat up.
Double check the water pump is functioning correctly, etc.
Also what oil are you using? Some put higher viscosity modern oils in older motors and they weren't designed for that. That increases viscous "friction" which means heat.
Another more exotic solution may be to use one of these new high heat transfer radiator liquids, but no experience in these motors, but have used elsewhere.

FYI: For the ATF guys. We did some tests and thinning ATF with 10-15% naptha or mineral spirits has better flow out/wetting than straight ATF. The published 50-50 ATF acetone mix as a sub for mystery oil is not one phase and will quickly separate on standing, plus it's vary flammable.
You can't really tell internal condition, if it just turns. That's playing the odds. It just a discriminator for big trouble or you're taking a chance with this one. Safest, but costliest, is to pull apart. A bore scope is a handy tool not found in most hobby tool boxes.

Anyone that thinks an '80s AMC Eagle is a "classic", sez it all.

Seat belts are a tricky issue because they weren't designed for them. There's some pretty hefty stresses to consider. These old large bumpered X frame cars tended to launch you through the windshield on impacts. Not much of an energy absorbing design like today.
If it's a state requirement, check with the state regulating body. There's way too much liability to comment on something like that from the internet.
My plan is to use race cars standards as I'm going non stock.
You have cosmetic/aesthetic considerations also.

Anyone could've painted it at some point. Depends to a point where the ivory shows. If the ivory is under another color it might be correct. If all color is worn off/missing and some ivory shows, it's more likely correct. If the ivory is over another paint layer, it's not.
If you take the wheel off*, look at the center parts, under the horn center or over the horn switch. It should be most intact or you can scrape at an angle to expose the color layers.
My '49 deluxe wheel was painted brown to match the brown basecoat of the wood grain dash/garnish trim. The plastic under the paint is darker "chocolate" brown. And there's those two chrome "wing patches" on the cross bars that were molded in.
* - a simple wheel puller can be made from a small >1/4" thick flat bar with two threaded holes to match the wheel threads and two long grade 8 bolts. I think there 3/8" fine or something.

That model creates 600 ftlbs in reverse and has a working range up to 350. For most auto applications that's twice as much as the most you'll ever need to torque anything.
So it's fine for snapping off bolts and stripping studs/threads. Not the precise tool you'll want for assembly. Even if you adjust it to deliver proper torque, I'd recommend to check with a torque wrench. Don't just go by the air settings. Some have a torque sequence that starts low and ramps up so it's not much use for those.
With alot of speed comes alot of heat and that can harm special tensile studs or bolts. Use a penetrating lubricant before breaking and oil on threads before tightening and adjust the torque spec for "wet" torque. Leave the impact on the shelf for tightening. Ok to run them up, but finish with a torque wrench.
Even lug nuts/bolts only need at most 120-150 ftlbs. Yeah, you can crank 'em on to max for a few cycles but eventually... Plus, on the road you have to loosen with a "wrench". So you don't want to hit 'em up full for that.
Most tire shops hire unskilled help and turn them loose with impact tools for speed. I had a flat on my trailer while on the road and I took it to the nearest branded tire dealer for a new tire since it was covered they rotated/balanced too. The tire jockey put the big dog on the alloy wheel lugnuts and stripped all the studs. Spec is a meager 75 ftlbs. I didn't find it out till I got home. I carry a torque wrench for wheel tightening when traveling.

I would not put too much confidence in comparing published auto company HP ratings. They were no "standards", independent rating orgs, and became mostly sales tools to match the competition. In the early days, even zero to sixty times where not known, which is a better indicator of true HP = Rate of work done.

I would investigate and correct the reason for the burned valves.
That often indicates running a lean condition for long periods going from memory. I'll probably be corrected rightly or wrongly by the others but I'm used to it. The L8 literature showed, I think two different materials for the inlet and exhaust valves. But that was also for leaded gas in the day to "lube" the valves. (I'm not a believer in that) You may want to upgrade all fuel system parts for today's crazy and future fuels.
We tend to assume everything was untouched/original after that long but that's rarely the case.