With the high voltage the power tube  can't be biased for proper class A operation. If instead of adding an LC filter you add an RC filter the hum will be reduced and the plate voltage lowered for more normal class A operation.  Current Limiting.  Find the line where B+ is as Underfiltered as possible, without getting too much of the subharmonics/ghost problem creeping in.  Elevate the heater supply to lower hum. Increase the screen, and the plate should decline slightly as a result.  Some of the hum comes from the voltage doubler B+ supply. Maybe a choke/capacitor pi filter?  Lower the filter caps in the preamp to 30uF.  For capacitors on the cathodes of the preamp tube, try 10uF for the first section and only 5uF on the second stage. 
   

  To soften the B+ rail a little you can use a dropping resistor after the FWB diode block.  Maybe something like a rheostat might work well.  Feedback pot also.

  Replace the ceramic signal caps with mica or film.  
  For channel 1 tone, just use the pull switch for a bit of treble rolloff (Plexi/Champ sound), no tone stack. Increase the value of R18 to give  Ch.1 more gain. Enough so it will overdrive.

  Ch. 2 should sound more VOXY if you change the tone stack 0.1u/0.047u caps to 0.022u, AND/OR change the bass control to Vox wiring which controls both bass and mids (turn the bass up, the mids go down, turn the bass down the mids come up.)  Move the tone stack between the distort (Ch2) channel and the power amp.  Anything else you can think of to Voxify Ch.2.

  Replace the input jacks. Add a jack for bypassing the reverb & channel switching.  Add a filament transformer, speaker jacks, & internal fan. It could probably benefit from shielded reverb cables. 

Ray Ivers did this:
 
1) Change R16 to 330K:   Smoother OD channel gain-control action, less OD, and less V1b
output loading at low gain-control settings. 
 
2) Jumper R21:    Not needed with new R16 value.
 
3) Remove C9:     More clean channel clarity and volume.
 
4) Replace R18 w/.002 uF cap.:  Clean channel bass boost, allowing bass tone control to be turned
down for better OD-channel tone.  I also ended up changing R10 (tone stack 'mid resistor') from 10K to 33K, which improved the OD sound a bit with the Strat-type guitar I was using for this mod (the owner's two main guitars are a Strat and a Tele). I measured about 7-8 watts clean output with a new Svetlana 6L6GC, and about 13 watts cranked.  The 125ESE sounds like an excellent OT choice to me, and would probably improve the power output and bass response.
 
SOMEONE ELSES IDEAS
 1. Remove C6 (750pf) & R11 (100k) - reduces clean channel brightness
 2. Remove C26 (180pf) - reduces brightness more
 3. Change R21 (220k) to 470k - makes the clean ch. break up sooner
 4. Change C12 (.68uf) to 3.3uf. - increases the bass response

4. Use a 500K A volume pot instead of 1m A. 

6. Use a 2 watt 1K screen resistor soldered right on
the tube socket.... in series from it's B+ supply

  Set the voltage so it will bias OK with an EL34. Use the screen resistors, though (100 ohm OR LESS). In the EL34, there's also the possibility of connecting the suppressor grid (pin 1) to the screen grid, for "slighty closer to true triode" operation.