here's how I would deal this, simple as is
- You make them movers, but the 'initial' state is not up there where the players start, but down down in the lava.
- So now you place them playerStarts somehow in some place where the players won't be able to reach them too often during the fight.
Like in some 'tube holes' in the ceiling or whatever .. not even really neccessary (see down below)
- Right under each playerStart you put a trigger that triggers each according mover to come up to its place like they are in the pics, that 'initial' position where the players should start.
- Now the round starts, the players spawn and trigger the movers to come up, the players land on them, and have 3 seconds or whatever time to grapple before the movers rush down into the lava again.
Thing is: the playerStarts shouldn't be too high above the 'initial' positions, because then ... you could as well leave out the movers 
That's mostly like it, and it's the only way I can figure it to work.
Because the problem with that Volume is that not allways one will fall down (in fact I believe this map will tend to end in time-overs with both players removed ..) but it
could possibly happen that they kill each other with the weapons, so no 'actor' would touch the volume. (dead bodys don't trigger ..)
Doing it like I described would asure the movers to be there where they should on every roundBeginn without needing any code or whatever.
Also I don't think it's too much of a problem if the players could trigger the movers during fight, because by that über-short time amount they would be hovering there they wouldn't make up much of an advantage for neither one.
You just give them a retriggerDelay so when someblody swings around one of the triggers again and again he won't cause the mover to flicker up and down ..
(but short enough so they can be retriggered at next roundBegin even when someone doesn't grapple at all and just falls down and dies)
Hope this helps; anyways, I'm sorry but I still think it's a funny idea that is, unfortunately, only funny for the first time you enter the map .. or someone else

Also with that room being up 8k U-nits high I don't think anybody can be
that slow with his grapple, only if he'd never played Chaos before
edit:
I was talking about using the meele weapons of course, with ranged weapons it kinda works

I just play tested it, and I like that design, lookin really nice.
I've got a different idea just right now, it somehow changes the map completely but .. somehow not ..
look:
You build a floor like where those movers are right now but you build that floor out of square movers (not too big, not too small) that act exactly like them movers in the map right now.
-> A player touches one square and has something like 3 seconds until it rushes down into the lava, so the players will have to be in constant movement, jumping and dodging around ..
After some seconds the square comes back up to take it's place in the 'floor' ..
Just an idea
