Tim,
Yes, quite probably the room will be a 'problem'. What you had was probably larger than needed but, I found anything smaller than 14x17 too small for a 3-way floorstander. However, I haven't heard the RM-1's in a small room so, they may hold together fairly well. I felt overwhelmed by the 'largeness' of the speakers I had. The imaging was incorrect and the sounds didnt' blend together well to form the proper harmonics of the instruments. I'd hear bass and treble sound separated instead of together.
You'll DEFINITELY need room treatment. If you have hardwood floors, you'll need even more. Good sound can be accomplished in a small room. You'll have to experiment with what you have, though.
My guess is that you'll end up with smaller speakers or stay in the larger room.
-C