These things can be fairly sensitive to relative orientation between the PT & the OT. You'll note, if you've looked at numbers of them, that virtually *all* hi-fi tube amps have the laminations of the PT and OT oriented 90 degrees apart. This was for anti-hum reasons, of course. Is either tranny open-frame, eg; not enclosed in a metal case? Most Triad low-wattage output trannies I can recall are that way, though most Triad PTs are enclosed. I have numbers of those open-frame output trannies (or similar) in the junkbox that are destined for small amp builds but I am generally reluctant to use open-frames for just this reason.
The short answer is, "do whatcha gotta do". You've apparently located the source of your hum, and so, you know that *nothing else* will cure it. Sometimes hum can be reduced by placing a grounded metal shield between the PT & OT, or, enclosing the OT in a metal box of some kind. I appreciate that you'd like neither since additional drilling is required, but as I said, you've found the problem and demonstrated the cure to yourself so thinking that it's something else is kind of fooling yourself. Perhaps it would be possible to buy an aluminum LMB-type metal box of the type used for small projects with the two "U" shaped sections that fit together to form a 6-sided enclosure and mount same using the same holes used by your OT so that no add'l drilling would be required.
Incidentally, the one absolute test for this is to substitute a SS rectifier. If the hum starts immediately on turn-on, eg; with no rectifier tube warmup, that's the culprit, no questions asked.