I didn't even have one drip on the floor.  However, the clearance between the bottom of the RT and the floor is not ideal, so it was very difficult to accomplish.  My thinking is that next time I will drive the front end of the RT onto my vehicle ramps, then lift the rear to be the same height (however I haven't done any research on the lift point for the rear).  This would give ample clearance making it not only much easier to remove the drain plugs, but also give me the opportunity to properly clean the bottom of the RT.
As far as removing the drain plugs; I used a torque wrench, which made it very easy.
I didn't have any issues filling the oil.  I use a funnel with a small orifice, so that forces me to keep the flow at a rate under that which the RT can accept.  At the rate I had to fill at, it took a while to add the 5.6qts.