No, the wires should be twisted, leave them. This is not your problem. What is the grounding on the filament supply? Does this build use the center tap of the filament supply, or does it use the two 100 ohm resistors to ground? The latter is better so change to this if you feel inclined, your call. Ken used the 100 ohm resistors, BTW.
Pull all three preamp tubes and turn the amp on. Still hum? Bad power tubes? Perhaps. Replace them and try this again. (BTW, eh, typically if an amp has been sitting more than 6 months the power supply caps need to reform. Do this by letting the amp run - unattended - for 4 hours or so. Put all the tubes back in then and turn all controls to '0'. Walk away...)
OK starting over then, pull the three preamp tubes and start this again.
Put the PI(V3) tube back in. Hum?
Put V2 in. Hum?
Put V1 in. Hum?
This will pretty much isolate your hum source. V1 can stand to have the wires leaving pins 2 and 7 sheilded. Is this your amp? If you heard the hum increase as you installed V1, then you can see the need for this. And sometimes the 25uf caps on pin 3 and 8 can go south which will cause a HUGE buzz. .......Which doesn't sound like your problem.
That's all I got. Reading your account of what you are discovering within the amp, the broken wire in particular, makes me wonder how this amp was stored. Is it in a head case? I would check all connections out at this point and it sounds like you are doing this. Carry on then.
Oh, some questions: Did this amp ever have a life without hum? Is this a new twist or are you just now just getting things sorted out? Do lawyers have better powers of recall than criminals?

Most people stall out when fixing a mistake that they've made. Why?