Well you could glue some rubber feet, like from an RO-20, or other plastic pieces onto the four corners of the probe. That way you can just rest it on the floor and push it. It'll just slide along and will always be the same distance. Attach that to a stick of some kind with the radeye and a 5ft bnc cable.
What I'm curious is what rooms are you planning to do this in? If you're using a 43-92 probe in a big room, scanning the whole floor would take forever. If there's dose in the room, how much dose are your ALARA guys willing to spend to do this? If there's not dose in the room why are you even doing it? Would probably be better off spending the money to do it properly. It'd be easier, faster, save dose, and probably a lot more accurate. Especially since floor monitors are gas proportional counters which are far more efficient than you're standard 43-92 probe. If this were a temporary thing then I can understand rigging something together. But if this is a permanent change then not buying the correct tool for the job is just lazy.
Honestly rather than a 43-92 you'd probably be better off grabbing a swiffer mop with a dry pad and run that over the whole room, then just survey the pad.