Well, dang, what a bummer. We’re all so different and I fear I can’t help, but I hope something I say does, at least a little!
I’m also a serious roadie, logging about 7K miles a year. I definitely know how to get aero on a bike.
My jailbird was iffy on a bike, and I abraded myself a few times and dealt with really bad scrotal burn all the time. Now I have a custom BAWR with a 57mm base ring and other changes and I’m much more comfortable. Yes, my balls and root are huge, even though I’m not overly well-endowed.
Anyway, it works for me one of two ways. First, I have a pair of bibs that is basically anatomically perfect- like a shaped cup from a bra (but for my parts). Wearing those, everything stays perfectly aligned. There’s enough room for me to get my forearms on the bar tops and ride that way, but I fear you’re not built the way I am or whatever and that won’t work for you. (I don’t know what the source of your discomfort is.)
My Rapha bibs aren’t so anatomically correct, and things don’t stay perfectly straight. That can be uncomfortable, but asymmetry wins and things move to one side or the other. So what works is a sort of John Holmes / Hamaconda deal where I tuck the cage and my balls down one leg a bit. Super comfy. Very distracting/imposing to look at, so things need to be realigned whenever I get off the bike.
In cooler weather I will take an old ankle sock with a good cuff and stuff everything into it. That seems to help with keeping things warmer and hence less retracted. Balls trying to crawl up inside due to cold temps and being prevented by the cage are unhappy balls.
Share more specifics about what is jamming you up, please.
Peace!