Ditto to tube pulling & headphone trick.
1. Tube pulling: If the hum disappears on standby with the tubes pulled, I would re-install the power tubes and see if hum returns. If yes, I would disconnect the power tube cathodes from ground*, to see if this affects hum. If disconnecting the cathodes from ground defeats hum, then use that type of standby circuit. Tubes can do weird things internally. E.g., heater hum may be completing a weak circuit through the cathode to ground, without the strength of plate voltage to pull the electrons the other way. In other words, I would take steps to
absolutely rule-out tubes. Also, there might be a fault in the standby circuit. If the standby circuit opens the B+ supply, make sure there really is -0- plate voltage on standby.
2. Headphone trick. The placement of the trannies may be causing them to induce hum in one another. So 1rebmem's suggestion for diagnosis may not dispose with the issue, unless the 24V PT is disconnected or even temporarily removed from the chassis. The placement of the OT & PT may also be an issue.
There is no absolution for hum.

It can happen to anyone on any build, including major manufacturers, no matter how many amps they've built.

At least your friend wasn't plagued with hum on his first builds! Did he use the headphone trick in determining the placement of these trannies? If not, he has invited the wrath of the gods!

If all our suggestions don't work, then the slight hum you describe may be caused by the OT itself. The ultimate solution for that is a potted tranny, but that's overkill for a guitar amp.
(*) unless the standby circuit already does this