Welcome to VK!
The set can have eventually some bad tube, or some misaligment?
Yes, some people even put ferrite antennas for less RFI. Same process; basically you use the same inductance from the corresponding coil (is good to measute also with a inductance meter). OR a little difference for compensate the shielded wire for it (needs to have very low capacitance if one needs to use shied cable to couple the antenna).
https://atrad-audio.co.nz/turneraudi...gineering.html
This guy are very serious about AM radios, is worth reading.