DSP based FMCW radar I have an SDR receiver I'm interested in making into a FMCW radar. The bandwidth is somewhat narrow as it only samples at 64 MSPS.

There is a problem in that without a bunch of embedded programming the RX and TX chains won't have their timing synchronized. Basically the up-conversion oscillator is synchronized but the DSP portion on the TX and RX lines won't be. 

What I'm wondering is, is there a way to use the initial signal sent from the transmitter and received by the receiver through direct LOS to establish timing offset for the reflected signal? Given that the RX and TX antenna will be close together you could use this to synchronize the system. 

Also I'm not sure what the processing would consist of though(or if it's even viable), most FMCW radar mix the transmitting signal with the reflected signal and then downconvert to produce to a local beat. I would be attempting to do this through DSP and have a much narrower bandwidth useable.
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.