Does the once-per-year rollover rule ever apply to Roth conversions?

No, and this confuses a lot of people. The IRS once-per-12-months rule applies only to indirect, 60-day rollovers between IRAs of the same type, where you receive a check and redeposit it. Roth conversions are not subject to it, so you can do as many conversions as you want in a year. Likewise, direct trustee-to-trustee transfers and rollovers from a 401(k) to an IRA are exempt from the once-per-year limit. The rule really only bites when you personally take possession of IRA money and try to roll it over more than once in a rolling 12-month period. To stay safe, always use direct transfers. Confirm the specifics at irs.gov.