What is the safe/proper way to run non-metallic conduit between floors?
This depends on your locality, and you didn't mention where you are. In my locality, I think the only necessary plug between floors is to use some fire-stop expanding foam insulation on the outside of the ENT. (For those not in the know, ENT = Electrical Nonmetallic Tubing, aka interior flex conduit.) 

Your local city/county building inspector / permit office will know more, and you should contact them.