I noticed today that I can put a breath mark in one staff and a fermata in another, and the fermata will perpetuate to all the other staves except those with breath marks in them. Ironically, this is what I wanted, although in the original version I used a caesura rather than a breath mark; but caesuras perpetuate to all staves, whereas the breath marks (as intended) do not.
The limitation is that you can’t have a caesura and a fermata in the same stave at precisely the same rhythmic position. The workaround is to set the grid to something small and place them at slightly different rhythmic locations.
Actually, Leo, I do not want the breath mark (or the caesura) and the fermata in the same part. I want the sustaining instruments to hold while the voice (and doubling flute) take a small pause for a breath. So in this case (even though the breath mark is on beat three and the fermata is on beat four–at least officially) the breath marks seems to override the fermati on any staff where a breath mark appears, which is what I want.
I only wish I could get the caesura to limit itself to one staff (and override the fermata); but I’ll settle for the breath mark. 
You could always create a custom playing technique that looks like a caesura, and apply that to only one stave, then (in Engrave mode) drag the nearby fermata off the page 
Yeah, I know. If it were important enough, I would. But in this case I guess I am lazy. If I find it affects performance, then I’ll make the change.
Thanks for the suggestion.