You know, the positioning of the shielded leads shouldn't be as much of an issue as you make it out to be...frankly, because they're shielded.

All my shielded leads from the 4 inputs and the volume pot are tucked under the board...and the amp is quiet.
Granted, you've mention that moving the leads above the board has improved things...so who am I to argue....anyway, a few suggestions to try:
*) Get some chopsticks (or other similar non-conductive sticks) and start playing around with lead dress. You might hit upon a wire lead that is the culprit. When you find it, either reroute, shorten or in a worst-case scenario...shield it. s2 has a downright ingenious method of shielding leads. He's been using stewmac copper tape. He runs the leads along the chassis and then tapes the leads to the chassis. Since the stewmac copper tape is conductive through the adhesive, it connects to the chassis and creates a ground that effectively 'shields' any leads that happen to be under the tape. I've been using monster brand guitar cable, which is thinner than regular guitar cords, but still quite thick...so the idea of my input leads taking up less room is really attractive. Using this copper tape method, you could literally shield everything in the amp....and it wouldn't really be too difficult to do so...
*) Tap components on your board with the chopsticks and see if you get any squealing or noise...you might have a bad solder joint or bad component.
*) On the idea of grounding, I see you're using a copper bus for the ground. Are all of your grounds solid and soldered well? With the amp off, tap each joint on the bus hard with something like a screwdriver or again, a chopstick....if the solder joint is suspect it might break lose on some minor abuse. I had this problem with one of my solder joints and I had to rectify the problem with a stronger soldering iron...
*) Twist the OT leads....it can't hurt. You can also twist the plate leads from the PI and the grid leads to the el84s...as those are out of phase with eachother. Dr. Z does this with his amps....I had a lightning build that gave me some trouble and I twisted anything I could that was out of phase and it certainly helped!
Most of all, be dilligent....we'll lick this!
-F