Thanks guys, I appreciate all of your input as every little tip or experience you've had can help point me to the ultimate solution. I have started removing some of my mods out of the circuit and will continue that process, but I can confirm that I am using the 27k NFB resistor, 2 Ohm tap, and 5k presence pot.
I figured I would try to locate the problem area further today by hooking up my oscilloscope. I found that when the amp is squealing (which again only happens when the guitar is close to the amp and presence control is up fairly high), there is an ~11kHz signal in the circuit. I was not able to detect it at the input jack nor between the 68K resistors and the grids of V1, but I don't know if that is because the oscilloscope is not good enough to detect a weak signal there or if there truly is no high frequency oscillation going on at those locations. Since there is no amplification at those points, I am assuming there is no oscillation going on there and that the scope is correct. I did, however, measure the ~11kHz signal on both sides of the V1 coupling caps, before and after the mixing resistors, at the 56k resistor following V2 pin 8, at the treble pot, etc. In other words, it seems like this high frequency signal shows up already at the plates of V1 and downstream from there.
I did notice something else strange - when I connected the amp to a dummy load, I could hear the squeal (no speakers attached) and depending on the position of the guitar, a putt putt sound as well. The 11kHz signal did not appear on any of the filter caps, but the small ~120Hz ripple remaining from the rectifying process appears to have been riding on a larger 20Hz voltage which I believe is the putt-putt sound I was hearing (20 cycles a second seems about right for what that sounded like). When backing the guitar away, the 20Hz disturbance disappears and only the 120Hz ripple remains. When I hooked the amp back up to the speakers, I was not able to measure that 20Hz disturbance at the filter caps, so I find the whole thing puzzling. I also don't understand what is physically making me hear the squeal with no speakers attached. I have to wonder how much damage I am doing to otherwise good components while troubleshooting this squeal!
On another note, I replaced some of the coupling caps and soldered in news ones in such a manner that they were positioned well away from other components. That did not help. I also moved some other wires around to no avail. I think my next steps will be to temporarily swap out the rest of the capacitors, look more closely at solder joints and possible grounding issues. When I built the amp, I isolated all of the pots and 3 of the input jacks so that the entire preamp section is grounded at only one location, Input 2 of the Normal channel. It was probably overkill, but I cannot see how that would cause the oscillation.
I read somewhere that a bad tube socket could cause squealing, but I am not sure how likely that is as in my case. Another thing I am wondering about is whether the OT itself could be causing this as the problem seems to only rear its head as I move the guitar close to the amp and to some degree it seems to happen within the same distance to the OT from whichever side I approach the amp with the guitar. I don't know enough to tell if this is a cause or effect, though. I do have a 2 Ohm Super Reverb OT that came out of my reissue Super Reverb before I gutted it. I could try and solder that in temporarily, perhaps?
Anyway, I guess there's plenty more to do, but if any of the above gives you other ideas, please keep sharing your thoughts!