I am a long ways from an expert on tubes but an RCA Tbe manual shows that the ratings of a 6X5 are virtually identical to a 6X4 except of course the “4” is a 7 pin miniature. Why not fabricate an adapter from an octal base and a 7 pin socket?
This makes two assumptions;
1: that you have the physical space and
2: that the 6X4 is a more reliable tube. (Is it?)
I have made a few of these adapters because I have some octal relay sockets that I use for breadboarding. The adapter can even be made for 9 pin miniatures like the 12AX7 if I limit it to a 6 volt heater connection. It would allow you to use and enjoy your radio and still not modify it.
Regards; John G.