I'm pretty sure this machine should run OK so long it has a good row of RAM in the furthest row from the EPROMs (front of the board). My way of doing RAM checks used to be to fit a known good set to this row, boot AppleCillin (or similar?) and let it burn-in test the other two rows. It was very good at detecting failures. Once I had a known good set in all three rows, I'd swap out the rearmost row (closest to the EPROMs) and fit the old set from the front row, the burn those in as well. It was pretty quick, but did depend on getting a good set in the front row. Not that that was difficult, most RAM failures in this row would prevent the machine from booting, so bad RAM here was obvious.
Edit: I believe that the 16k machines came from the factory with only the front row populated with 4116s. No HGR or HGR2 until you populated one or two more rows.