Not sure what a .510” bullet sizing die will accomplish? You do not for sure know that bullet/neck fit is the problem.....

Certainly seems to me that the prudent course of action is either a chamber cast or lampblack a sized case with bullet seated to really determine where the problem is. Otherwise you are flying in the dark.
Base diameter of a .450 3 1/4 from various sources is approximately .544”-.548” depending upon manufacturers tolerances, and if the case head/base diameter is just a skosh too large a machinist could easily make you a sizing ring to swage the offending area down a couple of thousandths.

I personally would not do it to a fine double rifle, but some guys would just get a SAMMI/CIP spec chamber reamer and relieve the chambers so as to fit current Hornady brass.

Just my 2¢

- Mike

EDIT: Just measured the case heads on both new Hornady brass and some 1920’s vintage .450 3 1/4 NfB.
Hornady = .543in front of the rim and .478” at neck with standard .458” jackets bullet seated
Kynoch original “Nitro for Black” = .542” in front of the rim and .490” at neck as factory loaded with original PP bullet.