DSP based FMCW radar
We did the same a couple of years back with what we called "echotimer", but not form FMCW, but for OFDM radar: basically, if you have a very large target that's very close and at 0 doppler, that's your crosstalk, and you can just subtract the distance of that.

Same applies here: with TX and RX hopefully sharing the LO, you're looking for a zero-velocity target that's close. You determine your range based on that, it represents your RX-TX time offset, and you just subtract.