Actually Bruce, there is no problem here because a conversion is not subject to the one rollover limitation. In fact, a conversion is a fall back strategy if a person has used up their one 60 day rollover, then realizes he cannot roll a TIRA distribution over to another TIRA. While doing a conversion is still taxable, it preserves the IRA money and upgrades the type of IRA. And for those under 59.5, it also erases the penalty on the distribution that otherwise could not be rolled over.
Again, the one rollover limit only applies to TIRA to TIRA rollovers, or Roth IRA to Roth IRA rollovers. It does not apply to conversions or rollovers from or to an employer plan.