What happens if you select JACK and tick the box for REAPER to start JACK?
I used to use a pair of old M-Audio Delta 2496 cards and had to use JACK to make them work with REAPER, but I used this line in REAPER's autostart JACK command box for audio setup.
You could try this line, replacing M2496,0 with your RME's device name.
/usr/bin/jackd -P80 -dalsa -dhw:M2496,0 -r44100 -p64 -n2 -Xseq
ALSA rides the closest to the audio hardware. JACK and Pulse ride on top of ALSA.