A cheat around the network issue (if needed) is to use Bluetooth. Of course, you may have to install a bluetooth adapter in the desktop PC you're using for the projector (unless it's a laptop already equipped with BT). BT adapters are almost literally a dime a dozen. Pairing the desktop with the SP3 may take a little patience, but you can definitely do it. I don't know how well the various remote desktop solutions mentioned above will interact via BT, but as I mentioned earlier, I have used it with the MS Remote Desktop Connection tool without issue.
Just one more suggestion.