1st, my proposal below is based on wild speculation and not real world experience, but perhaps the others will weigh in on any pros or cons.
I think you would be better off with 1 mic receiver in the room with the mic, output that to a small mixer, then go out from the mixer to one of your lav mic setups that you mentioned to use for a wireless speaker setup. You might be able run a wire from the mixer to near the doorway and locate the lav mic transmitter there, then in the other room put the receiver from the lav mic near the doorway there.