Actually, CoC would be your only recourse here. FAA doesn't force airlines to compensate with sub 56 seat (that's the number) IDB for weight and balance, but a separate CoC section could make United contractually obligated to do so (which I believe they do).

Going further, especially now that oil has come back up again, the W&B rule needs to be reexamined in light of the fact that airlines frequently tanker fuel between airports to save money. While this means little on a larger jet, where W&B won't matter as much anyway, OO is known to also practice tankering even on its Brasilias. If they are restricting to, say, 27 because of the weight of the extra fuel, that is not a safety issue.