What house rules/modifications have you adopted to make a board game work well over webcam?
We played Monopoly with a single board. 

It was useful to have dice, money, and property cards for the remote player at their location. Locally we ghost played them - they rolled remote dice, we trusted their reported roll and moved their counter on our local board. We also did their money for them so local players could see it, but they duplicated that at their end. When doing transactions, they picked out the money from their remote stash and showed it to the camera (the bank acted as interchange).

Money and property names differed in the versions we had so we went through before hand to check the money was "normalised" (used an exchange rate of 1000). Properties were named by colour Brown1 being the first space after, and Purple2 being the last space before Go. Mention of a property at the local end was followed always by its list price.

Worked well, 2 local and 1 remote player using meet.jit.si for a 4hr game (including setup).