Thanks to Sheila for bringing this to my attention. I haven't been on the forums much lately so I wouldn't have seen this if not for the nice note she sent me.
I honestly don't have any immediate recommendations for you. It sounds like hip flexion increases the intra-pelvic pressure and makes things worse, so decreasing the amount of hip flexion required through the pedal stroke might help. I'm just thinking out loud here.
Have you had a bike fit before? Are there other positions other than squatting that seem to aggravate the venous distention/
I'm going to let this percolate and see what I can come up with. I'm also going to talk to a colleague who does a lot of pelvic floor work and is also a cyclist. It would be interesting to see what she comes up with.
Living life like there's no tomorrow.
http://gorgebikefitter.com/
2007 Look Dura Ace
2010 Custom Tonic cross with discs, SRAM
2012 Moots YBB 2 x 10 Shimano XTR
2014 Soma B-Side SS