A few potential points that would have been useful for me on my trip last weekend (all in NC):
US70: Beston Rd on the east side of Goldsboro — serves as a shortcut to Piney Grove Church Rd, which already has a point on the route (PGChuRd); would be more than a mile away from any other point
NC41/NC111: Jackson Store Rd south of Beulaville — serves as a shortcut and already has a point at its other intersection with NC111 (JacStoRd), would likely require renaming that other point to disambiguate
NC53: either Nine Mile Rd or Gurganus Rd between Maple Hill and Jacksonville — would break up a 7+ mile segment (SycSprRd to HarCrkRd). I actually used Nine Mile Rd, but Gurganus is close enough and arguably more important.