As a repair tech myself that has thousands of hrs on the bench I can attest to a number of transformers spoiled because the owner tried to operate the amplifier with a fault. Usually a bad power supply cap. You unfortunately are no judge of how the amplifier was operated before it hit your bench and thus cannot come forth with an analysis based on something you simply do not know.
I would be more than happy to supply real honest to goodness infrared temperature readings of the transformer under different operating conditions.
The last eight or so 70's I have sold have been modified with an honest to goodness power supply. Power supply add on board, diode mods, different front end, individual tube bias adjustment, three wire power cord, and a single triode switch. They are all still running and the owners have no problem running 2)6sj7's and 2) 6sl7's some boards running 6SL7's and 6SN7's plus KT88's or 6550's.
Now, instead of just pointing the finger I have actual experience running the different modifications. Yes, I had one large power transformer on an abortion of an amp I bought that used 4) 6dj8's in the driver board. I ran cool alright and for those faint at heart go for it.