I don’t know if it will sound great, depending on how many weird keys they plan to cycle through and how the voicing of the arrangement looks, but you could try just playing whatever notes from the chords you do have.
. I.e. if you’re looking at an A major chord, play just the A and the E, and leave the C# out. Or if you’re looking at a C# major, just play the F and leave the root C# and fifth G# off.