So I ask the guitarist to bring a 'nice' guitar...

i have one guitar with floyd rose and one with prs tremolo and it works the same on both even with using the tremolo..maybe divebombs work not so great...

My cocern is about the floating one. Normally when you break the balence between the springs and strings tension it will go out of tune. So when I use capo with my Jackson, the strings go cents out of tune, making impossible to record.
 
when bands bring in guitars with floating bridges for rhythm work i just block off the trem with a bunch of coins taped together. works a charm, usually doesnt take me more than 5 minutes.