[jerryhawthorne]

Matt, your doing fine. Repairing these beasts requires a bit of a structured approach. First "iron" the fact you have hum indicates the major iron is just fine, speaker/output transformer and power transformer. Great.
This type of radio is "relatively" simple, a bit like a guitar amp. Volume on the front end (antenna) amplification of the RF signal for several stages to perk up the signal then on to a detector tube to strip the audio off of the RF signal. Just a diode like in a crystal set.
Once that is done you have audio (AF) which the output stage will amplify for the speaker. You need to address the hum. It could be coming from almost anywhere, hence pulling tubes on at a time.
The audio amp runs flat out as the volume control is not on it but on the antenna. Just an FYI. Volume is controlled in the antenna section, far before the signal is turned into audio.
I'm not familiar with the regen type radios but seems they get additional gain out of the RF section by feeding back the signal for another pass through for more gain on the cheap. Hence perhaps alignment might be more critical to assure they are passed back for amplification properly. Not proper, squealing as the signals are not in sync properly. No doubt wrong about that part but my simple take on it.
Have some fun. I'm learning as well as you.
Best, Jerry
PS: do check all coils in circuit. Should be very low resistance.