Thanks, guys -
I have found that 3M SMR (oops, swirl Mark remover) will leave a haze too, but if you apply like Cybercowboy says, going to successively lighter pressure with an orbital, it works pretty well. (I wrote this up in "technique matters" a few days back.
I didn't find this to be the case with Finesse-it - but again, I just think I misunderstood its purpose. I will treat it now as a step HARSHER than swirl mark remover, and expect it to make haze. If it cuts well, then so what . It just needs to be followed with SMR, then hand polish (if I use it at all. I'm thinking of having an "opened and slightly used " sale........)