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.

Amazing to see that post, BDC. Truly a museum-worthy piece!

You should avoid gas with ethanol in it as it can damage plastic/rubber fuel system parts. That being said, I doubt that Packards have many such parts aside from things like the carburetor gaskets and probably the fuel gauge float. Aside from that it doesn't really matter. The average octane when these cars were new is less than octanes today so I'd be surprised if they have any problems using even the lowest grade of automotive gasoline in your country.

Likewise for the 50's Clipper skirts. Most of the brochure photos show them but they seem very uncommon to have today.

https://packardinfo.com/xoops/html/downloads/1955_2GreatLinesBrochure.pdf

I know Ross just parted out a '53 Clipper some months ago. He would be good to ask.

https://packardinfo.com/xoops/html/userinfo.php?uid=618

Looks like it would have been quite a ride back in the day! To be honest I have no idea the year or model just looking at it, but I know there's people on here that would.