No state party has a right to compel its state to hold a primary election for Presidential delegates, nor can be compelled by a state to choose its Presidential delegates by primary.
Michigan GOP will simply have to schedule caucuses at a time compliant with RNC rules.
(Interestingly, in most states, the state CAN compel a party to choose its candidates for other offices by primary, or simply do away with the party choosing its candidates in any meaningful sense in favor of open primaries, jungle primaries and single transferable vote regimes.)
bttt