The floors aren't particularly slick unless there is water involved. Your shoes (which are the same ones I wear) should be fine.
I think a rickshaw would work wonderfully.
Another thought, and I hesitate to even suggest it, is to get someone who is very good on skates (I have done this as I played hockey for about 8 years) to follow on a ronin or movi. You can get some very cool stuff that is difficult on steadi (unless you have a grip pushing you really fast on a ricksaw)
My last thought is this: I have used a dolly on a skating rink as well, the floor is almost as good as dancefloor if not as good. Very suitable to do complex moves on dolly.