For those interested and/or encountering something similar in other designs, the problem is solved, while retaining relay true bypass. For starters, I moved the output XLR connector about six inches away from the input on the rear panel. I also placed the second bypass relay (DPDT for the +/- output) on a small daughterboard (pad-per-hole vector board) directly at the XLR output, connected to PCB via Mogami twisted pair. All is well.
Radardoug, if you're reading this, hear me out and please correct me if my logic is flawed! Here's why I decided to stick with two DPDTs for true bypass: I was thinking that if I used one DPDT switching at the output only, the output of the previous device in the signal chain will be seeing the 600Ω load of the attenuator in parallel with whatever device comes after the compressor.
Same with employing a DPDT only at the input: I would imagine any preceding device's output would see the secondary of the output transformer as a load in parallel with the input of the next device in the chain.
Either way, I don't necessarily want the device to present any kind of load when in "true bypass."