Spinning opposite wheels off-road. Any mods to solve it?

Had my XC70 on a trail and came to a nasty rut I tried to cross and ended up with the back passenger tire in the air and the front drivers wheel digging dirt. Was able to back out but I put the car there again to see if it could get through in any way. DSTC off, spinning the tires with no grip only. DSTC on, spinning the tires with no grip. I tried this at various rpm, auto and manual, and left foot pumping the brake a bit to try to get the TC to kick in but it wouldn’t.
So, are older volvos just incapable of braking opposite wheels to get themselves out of these situations like modern crossover / off road AWD systems? Next, is there anything modifiable to fix this on a P3? I was thinking limited slip diffs, but I thought that was only a P2 thing.