I might be wrong, but I actually think that random initial phase offset between two RX channels is quite normal and expected thing. Such offset should stay constant during operation, though.
I think that one should implement simple proof of concept in GNU Radio to make things clear, such as forcing TDD mode, transmitting some QPSK signal via one TX channel and receiving it via both RX channels at the same frequency. If everything works as expected, we should be able to see non-rotating QPSK constellation of signals obtained from both RX channels (while initial constellation angle may vary for different program runs). Only thing which is non-trivial as it comes to creating such flowgraph in GNU Radio is forcing TDD mode (so that TX and RX chains will be driven by the same LO). @IgnasJ, any ideas how to do this in a simple way?