Existing effects can increase the cost of the next song or dance.
Using a Song or Dance while other Song/Dance effects are active increases MP consumption. Cross-type stacking also matters: an existing Dance can increase the next Song's cost.
Interlude adds Inner Rhythm for Sword Muse and Spectral Dancer at level 78, reducing Song/Dance MP consumption.
Decide which Songs and Dances the party needs before the first cycle, then coordinate their refresh. Existing effects can make another cast more expensive, including when the previous effect came from the other support. Recasting one effect casually can therefore change the MP needed for the following casts. Watch the actual MP used in your current sequence rather than budgeting every cast at its isolated base cost.
Song of Warding supplies party magic defense; Dance of the Mystic supplies party magic attack. Those are different reasons to spend support MP. Dance of the Mystic also requires equipped dual swords. If that dance cannot be cast, check the weapon requirement as well as available MP; receiving another Song is not a substitute for the required equipment.