You may have found the answer by now, but I had the same problem with an Oregon Scientific WMR200.
The USB-to-ethernet adapters I sourced don’t work on a network, they are actually USB-to-ethernet-cable adapters, so you still need a physical Cat.5e cable from one location to the other. But at least it can be longer than the max USB allows!
I didn’t look too hard for a wireless solution, given all the problems I have with wireless reception in this house!