Yeah, making the core x-section smaller is... a challenge. I wouldn't expect anything exotic materials-wise from Edcor.Well, wiring insulation has come a long way, and you can fit more turns in the winding window now than you could 50 years ago because the insulation is thinner. This insulation is also far more tolerant of heat stress, so a modern power transformer can be run hot to the touch and the internal wiring still has a substantial amount of thermal headroom remaining. We do have more variety of lam alloys available as well, though some of that stuff gets very expensive very quickly.
A smart designer might use a modulated high frequency carrier to get the output transformer size down. A really smart designer would use a transformer simulant like switching impedance converters. The only Carver tube schematic I've seen was for the Silver Seven, and the circuit was utterly 1955 conventional (looked like a Mullard variant).