The Gen3 Sub features the latest radio so it might be marginally better, but I wouldn’t bet the purchase price of a new Sub on it.
Your fundamental problem is that the Sub -- or any other home theatre satellite -- was not designed to be used in a different room from the master player. It connects to the master -- the Amp in your case -- by a local, direct 5GHz link. This clearly suffers from attenuation if there are walls and floors in between.
Presumably the Amps are wired to the network. The best option would therefore be to run a wired connection to the Sub as well.