EL34, 6CA7 and KT77 all have the same functional pinout, so don’t know why adapters would be needed.
EL34s and small bottle 6CA7s are pentodes with suppressor G3 brought out on pin 1.
Big bottle 6CA7s and KT77s are beam power tubes. NOS and Russian reissue tubes are tetrodes and have the beam forming plates internally tied to the cathode. JJ 6CA7s and KT77s are beam power pentodes which the beam forming plates are brought out on pin 1 for external connection. Depending on the circuit these JJ tubes may cause problems if the beam forming plates are not connected to cathode potential.
Justin at Headamp explicitly says NOT to use the KT77 in his BHSE amps. SO DON’T USE THEM IN HIS AMPS.
I’m currently using a quad Gold Lion KT77s in my GG, and liking them a lot. The opto-servo in the GG might be the reason they work here (so far.....). Does not necessarily mean they will work as a EL34 replacement in all cases.