Yes, bad connection to the socket could cause squealing.
The power tube heaters are all in series, so you need to verify all the socket solder joints, and verify the socket pins are contacting the tube pins.
Your description of the tube holder being loose sounds like the socket pins need to be retensioned.

If the volume is up, even with a grounded input you will get hum waving your hand around the input area of an open chassis.

  That waveform does look like something a bad cap could cause.  Do you see that kind of waveform on any of the supply rails?

Not sure if you mean little caps, or maybe SMT caps.
I don't often measure little caps, or any other for that matter.  More likely to find bad ones from fault symptoms and in circuit measurements.
But they do have their uses, and having the right tools for the job is very valuable when required.
I have a DE-5000 LCR meter that is well regarded and relatively inexpensive.  But you need to make sure you get the clips, or SMT tweezers if you need them.  I made the mistake of thinking I could use regular probes and ended up having to buy the right ones.  Would have been cheaper to get them all together.

 Instead of lifting C46, ground it's end that connects to Fet3.  Any effect on the hum?
The unrectified AC that is feeding the relay and Fets is for turn on muting.
When you say there is large or nasty hum on supply rails, please provide numbers you have measured.

  In the meantime, you can put a non-electrolytic capacitor in series with your meter probe to block the DC when measuring AC.  Something like .1uf with a sufficient voltage rating for the highest voltage you will measure, I would use 600V if you have it.

  The voltages will read high if the tubes are not installed.

  Can you verify that it is not some vibration caused by the high volume that is triggering the problem?
Running guitar into FX return, if you give the cab a good solid thump (with palm or rubber mallet or what have you), does it affect the symptom?

Otherwise, maybe others here can comment whether the 100mA bias sounds correct.

  Now you reminded me of a show we used to get up here when we were kids, "skippy the bush kangaroo" 
  We got a bit of a freak snowstorm here yesterday, just to remind us it's not quite spring yet.
  Cold and frosty you say?
https://www.youtube.com/watch?v=8BngJKGZe1k

An open R87 or R89 could also shut off current through Q11.

  You said it sounds better in the low input.  This implies the preamp stages of the Traynor are being overloaded.  Have you tried lowering the output level of the fuzz?

Quote from: Roly on April 30, 2015, 11:54:35 PM
a runcible arrangement IMO).

Sorry but I will sidetrack here a moment.
I'd never seen that word "runcible" before and had to look it up.  Now I know how Roly meant it, but I also see the word has been hijacked for a very interesting product.  They call it an "anti-smartphone" so I guess that makes it a "dumb-phone"  .
The ideas and philosophy behind it are quite interesting and inspire a little bit of optimism for me as far as tech for future generations go.  Of course it may just be a way for someone to make lots of money, but "dreaming is free" as she said. 
http://mono.hm/runcible.html

  Yes, you can get the full power of the amp into a pair of cabs, both getting full frequencies.
It will be 200W per side at 4 ohms for a total of 400W.
So no advantage to going bridged unless you need to get the full 400W into a single 8 ohm speaker.
The balance pot is 0026416, knob is 0026402.  They may not be available anymore so you may need to contact Fender and ask if they have any numbers for substitutes.
  Worst case, if you are going to use mono with balance centred anyway, you can set what's left of the pot, or use resistors.

 In addition to the gain issue Enzo mentioned, treble response will also have a big effect on the amount of hiss.  So if you find that Fender has more hiss than some other amp, maybe the other amp doesn't have as good high frequency response.  Maybe adjusting the treble controls on the two amp will make them more similar in terms of hiss.

  These are nice amps for servicing and quite reliable.
I'll start from the other angle and ask whether this is practical.  You will need a cab that is rated for 400watts at double the impedance of what the minimum is for each channel.  I'm pretty sure the minimum is 4ohms per channel.  So you need an 8ohm cab rated for 400watts or better.
  Now what's the chance it's a single speaker in that cab?  If it isn't, the easiest thing is to rewired the cab into 2 banks of speakers with 2 inputs.  Now you can get full power into a single cab.
  Otherwise, it's bi-amp capable, but also has a switch for mono, so the 2 amps are the same as Enzo mentioned.
  No big deal to make an adapter cable for the outputs, but you still need an inversion of one of the input signals.  This would probably be possible by reconfiguring the biamp mode.