Don't bother trying to fix the old tank. Just get a new one. There are new reproductions available for '51-56 Packards. They all used the same tank.
Auto City Classics:
https://www.autocityclassic.com/51-56%20Packard%20Tank%20TS5156PK I believe Kanter has them too. Pretty sure both come from the same supplier in Taiwan. $450 is a good price for a brand new tank, fresh metal, fresh paint on the outside, and zero problems with rust and fouled fuel. Just buy the tank, rebuild the carb, and plan to rebuild the fuel pump (if it hasn't already been done). Then you'll essentially have all new fuel parts (except for the main line) and will never have to worry about fuel again.
On that note, get a new sender with the tank. But be sure to test the float on it first. I have a new sender but it has never worked right, and I've done all the proper tests and grounds. I believe my float has a leak in it. Best to check it all before hand. Dropping the tank over and over again is not fun.
-Kevin
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