Dave,
Base 2 and Base 3 (and Base 1 for that matter) do not interact with the power feed to the tracks in any appreciable way, unless you're using a PowerMaster, or similar feature in the ZW-C or ZW-L, in order to control track voltage from your Cab x.
They simply transmit radio signals. These are very low power and so can't affect the track power in any substantial way, of and by themselves.
What you describe appears to be a coincidence, unless you're also using a PowerMaster or the ZW-C/L's PowerMaster feature.
So, I suggest that you check your tracks, engines, and rolling stock for a short circuit or heavy load that somehow appeared while you were installing the Base 3. At a minimum recheck every wire you removed, and then reinstalled, during the transfer.
Mike