"Does this amount carry forward as the basis for next year's 8606?"

This was a pro rata taxable conversion, then? A "backdoor" is done to avoid tax, because it is done on fully nondeductible account balances. When other funds exist in Trad, SIMPLE or SEP, and there is no full conversion (only basis exists), then that would be Backdoor. It seems your taxpayer has the scenario where each conversion will slightly reduce Basis, because each conversion is a % taxable and a % Basis.