Yes, thanks everyone for helpful solutions! Good catch on the active input Mark!
The "input setting" in the proj menu was set to "RGB auto" which should have solved it - but all the switches I was changing were settings FOR the inputs, which I mistakenly thought was switching WHICH input was active. So eventually in the manual I discovered that the only way to change inputs was using the remote, and the only way to get the remote to work was to physically pull out / extend the XLR cable port, which activated the IR remote function (yeesh!). (Not having an XLR cable in the box, it took us a while to figure out how to get the IR working...).
The manual was a bit unclear because the actual input ports are optional at the factory, as in each port can be swapped out physically - so the modularity meant the manual was a bit more ambiguous to me than it might have been.
Even a phone call to the rental house didn't catch what we were doing wrong. They had nicely sent a guy out to help us but we figured it out before they arrived, and we turned them back home!
We ran VGA cable and skipped the Extron box.