Cimex are probably the preferred "rotary" for all CC's but the cost can be prohibitive.
They are large, heavy and cumbersome and I personally wouldn't use one as a main tool for residentials. For commercials they're great as long as there's enough space around and beneath desks etc.
When used within a multi-system clean, the preferred way tends to be to rinse/extract first in the normal way, then encap and leave. You need the encap to encapsulate soil and then dry. Having said that, some do encap first then rinse. It's better to use a lower foaming encap solution for this. I have tried Prochem's encap and found it worked well in an LM situation, but it didn't foam up like some others I've used, so this may be suitable for a low foaming rinse, but make sure you have some defoamer just incase. Otherwise, just trial different brands.
Safe and happy cleaning

Ken