Are there extant copies?

I'm not sure what you mean to be honest.

What state is the car in? What state is it titled in (if you know)?

In some states like PA it is very difficult to title an untitled or defectively titled car. As a fix, people will buy a junker car of a similar model for cheap that has a clean title, and put the junker's plate on their good car, and register it with that title, knowing that no government/police/insurance official will be able to tell the difference. It's extremely common in some states and I think this is what you have.

Look carefully for damage to the plate around the rivets, bends in the plate that were flattened back out, and rivets of non-original type (like blind rivets).

In my opinion, normally it's "safe" to buy an OLD car like this. If you see something similar on a car made in the past 25 years, run away. But for old cars, many of which have lost titles or even were not required to be titled when purchased (NY state only required them starting 1971, for example), it's pretty common for states where you can't get bonded titles (1/3 of them).

Ah yeah, not sure why I was confused when you said "exhaust valve"; it's the right word.

Glad to hear oil pump is ok.

Yeah that looks like a BIG project for sure, challenging for even an experienced restorer. I say this because I don't want you to feel too bad giving up this potential project. IMHO it's best to start with something mostly intact but non-functional, so getting it going is the only necessary challenge. In the Packard world even these are cheap (not buying a barn find '55 T-bird for example).

It's tough to find cars to fix up at the right "difficulty level" for a beginner. The easy flips tend to get bought up the fastest, after all. Just wanted to chime in my and best of luck with any future projects.

Fair point Don, to me it's worth considering that those options were $700 each in today's money; maybe not worth it if you're only driving it a couple times per year. And Spokane is not exactly warm, fair weather most of the year either. Obviously a Patrician is not cheap but, eh, save money where you can? I would imagine the dealer just ordered it in that way.

Marty, for me one aspect is: if any of us owned this car we would probably be fixing every little thing and making it concours ready. But if you owned a car for 70+ years and did only preventative or necessary maintenance, this is probably how it would end up. Wiper motor not working from old rubber, the capacitors in the radio and clock probably blown from age (electronics usually last only a couple decades even in the most stable environment before a capacitor failure), radio vibrator froze up from disuse, who knows. Even though each of these costs only a few hundred dollars to fix, for a car that's worth only $15k you wouldn't fix them if you're flipping it. Even at the time most of these were off the road in like half a decade so as reliable as these older cars are in some ways, no one designing the accessories cared about multi-decade longevity, same as in today's cars even. Anything from the 90's and up will be an absolute nightmare to keep on the road in 40+ years due to the computer systems failing. I wouldn't be surprised if in 50 years there are more 60's cars on the road than 90's cars. Whether the odometer was rolled back or not, this seems like a normal amount of failures for a car of the Packard era. Obviously no hard feelings all around.

Not cleaning that stain on the front bench just seems lazy to me, though...

Check these sites if not already:
https://www.kanter.com/packard/
https://www.packardparts.org/

I doubt that you will find what you need as a kit, as it seems there are more junker Packards with salvaged engines than the other way around. To me it doesn't seem that full rebuilds are terribly common, so you'll probably need to source parts individually if that is all you need.

However: FULL rebuild kit is for sale for $1619:https://www.kanter.com/packard/pac-556.html#5
•8 pistons with pins and clips
•piston ring set
•overhaul gasket set
•cam bearings
•main bearings
•rod bearings
•valve springs
•timing chain and gears set
•freeze plug set
•valve lifters
•engine pre-lube

For individual parts:

Gaskets:https://www.packardparts.org/products/packard-gaskets/
Pistons $69 ea., Timing Chain $60 is here:https://www.kanter.com/packard/pac-556.html#5

Oil pump you may need to ask around to guys like Ross.

Not 100% sure what you mean by "exhaust valve" or "rig".

For a cast part, it would probably be more economical to 3D print a replacement on a metal 3D printer.

Apparently metal 3D printed parts cost around $200 per pound to make. Only significant 1-time cost is making the CAD model for them.

Yeah the headlight switches are a known sore spot in Packards, they always go bad eventually and are very difficult to remove/repair.

Unrelated: I was browsing Rolls-Royce listings on Facebook and found this!

https://www.facebook.com/marketplace/item/435624181342077/

Fair point, most of the car does seem to be in pretty good shape, though it is a bit odd that the radio, clock, etc. don't work. To be honest mine don't work either ('55 Clipper) but it's in a lot rougher shape overall.

Something interesting is on image 28, the driver's door armrest looks to be in worse shape than the armrest on daily driver, a Chevy Traverse with 160k miles.

But then on image 91 it reads 3821 miles in October '76, then image 30 says only 26 more miles in May '78. And IMHO the pedals and driver's floor mat shown in image 51 don't look like 100k miles of wear.

Another place specifically on Packards with this dash is that the area around under the starter will get worn from people's keychains hanging around, which this one doesn't (image 46). Not necessarily the best metric as some people use a separate car keychain, but it's something I look at.

To me it would seem to be a low mileage car. The other thing I would check, but not clear in the photos, is the amount of wear on the body-side door latches. IDK about '56 but for the '55 year they will always show an extreme amount of wear by 100k.

To me the engine compartment doesn't look bad for almost 70 years old and splash shields look normal. We may have to agree to disagree.