I will say that it is very, very, very rare to blow a PT. OK, an original may fail, 50 year old part. *Still* rare. You throw in another and there's a fault. I would suspect you'd have 5-10 seconds of stinky-smoky-smelly (which should definitely blow the fuse, but let's say there's a 10 amp NO-BLO fuse in there) and if you didn't get to the on/off switch in that time you *could* burn out the new PT. But if you caught it after only 1-2 seconds of stink/smoke, most of the time they will survive that.
Must employ a light bulb limiter/variac, that's too costly a part to blow off. Oh, and be sure the right fuse is in there, but don't blow off 5 fuses one after another. They too, cost money nowadays.
This is an unusual circumstance. You really cannot detect many of the faults that would plausibly cause this just measuring the tranny, as the DC ohms on the 5 volt winding and 6.3 winding look darn near a short. However, I would take the bad one or ones and compare the ohms readings on the various windings to the new one. That could give you a clue as to what part of the amp circuitry is shorted. Next time, at minimum power up the tranny before you even mount it in the chassis, with no load, with your meter leads clipped to the wire ends *before* you power it up. Take readings. Unplug. Go to another winding.
Try the amp with a different rectifier tube, that's definitely a valid idea. And NO rectifier tube. Got a 5Y3? If so, that's a valid temp substitute that will lower your B+ by 35-40 volts relative to a GZ34. That cannot hurt you and a junky old 5Y3 is a cheap tube. Maybe you have a shorted GZ34...in fact...that possibility hereby jumps to the top of my possibility list.
He's not plugging it into a 220 VAC outlet?