I did some further tests and my NROM socketed test ReproX board can run Dig Dug and Championship Lode Runner, which are both NROM-128, but can't run Super Mario Bros or Chubby Cherub, which are NROM-256. This page suggests that the mirroring is different:
http://wiki.nesdev.com/w/index.php/Programming_NROM and that NROM-128 games mirror at $C000 and $8000 but generally run from $C000-$FFFF range while NROM-256 run only from $8000-$FFFF. If the PCB, as configured for NROM, only maps the PRG ROM to $C000, then only NROM-128 games would work--which is what seems to be happening. Or, possibly, one of the jumpers already handles this, and I really suck at soldering.