Recommend the Diamondback Auburn Deluxe tubeless radials. They are made in the vintage sizes.

Remove the pump and watch for play between the arm and the diaphragm(s).

The preferred way to lower the front end of a car with independent front suspension is with modified spindles. These "lowering spindles" will lower the front end while still providing the stock play in the suspension. Probably not available for Packards.

It could be worn linkage too. Easy enough to check.

There have been some posts here cautioning not to use distilled water as it can leach some metals in the cooling system. I have use de-mineralized water which is available in most super markets. We used to call it "ironing water" as it was used in steam irons. It did not leave mineral deposits which would clog the iron's steam ports. Of course, no one irons clothes anymore.

Mineral Spirits is a good and safe parts cleaner.

Howard posted a 5/64 hole not a 5/32.

I had success in stopping vapor lock in my 47 Custom by adding a small amount of Diesel. A five percent amount worked well with no odor or smoking from the Diesel.

The underwood temperature in that car was probably a primary cause. I would need to use a rag to lift the hood to prevent burning my hand. The engine coolant temperature was in the normal range and the engine never overheated. But the high under hood temperature was something I had not experienced in any other car.

I had the same problem with my 55 Clipper (coil and leaf spring suspension). Changing the brake light switch fixed the problem. Some switches do not play well with silicone (DOT5) fluid.

Daniel Schmitt & Co. has it listed. Looks like a very nice Packard.