Simple crosstalk cancellation (or signal separation)?
If I understand correctly what you are trying to achieve is usually called Acoustic Echo Cancellation. In many cases, so-called adaptive filtering algorithms, such as the (normalized) least-mean-squares ([N]LMS) algorithm, can be used effectively. In this context, I can really recommend the book Adaptive Signal Processing by Widrow and Stearns. I'm sure you'll find a number of ready-to-use implementations of the (N)LMS algorithm to experiment with on the internet. (Have an eye on the filter order - it needs to be high enough to capture the length of your crosstalk path.)

Furthermore, as you mentioned that you are already working in the frequency domain, you can have a look on algorithms that are called (you guessed it) frequency-domain LMS algorithms. They originate, via so-called block LMS algorithms, from the classical LMS algorithms. In this context, I really liked the paper by Shynk: Frequency-domain and multirate adaptive filtering.