What's the input drive end of those Puma live tools look like? I think a male tang, that doesn't look unlike the tang of a Morse taper tool. The drive shaft, inside the turret with the female slot, they have clearance, so the tools can pass through as the turret rotates. Normally about 0.1mm (4 thou) per side. That wouldn't translate to 2 - 5 degrees of lash, but there's some clearance there. You can always feel it, but once its turning it should take all that up.
That drive shaft inside the turret. Its alignment is often over looked, when you pull taper pins and do an alignment of the turret drum. You can move the turret, but you have to check that the drive shaft is looking at the tooling hole.
If your bearings are really shagged, and things are floating, you're also loosing mesh across the helical bevel gears.
I'm not aware of any coupling that's inside them, that can be replaced, and I've been inside hundreds of them.
You'd have set a dial test indicator on both the input and out side of the live tool to check for internal clearance. Because the input shaft / tang is so small, I'd use our version of a tenth clock. And a half thou or thou at a larger diameter, some where out at a larger diameter, like a notch in a tightened ER nut. When I have to re-mesh those right angle drives, I leave nearly a thou tooth mesh clearance. There has to be some clearance, other wise they tighten up when they get warm.
Regards Phil