@8th-note
I really like your approach!
As noted by others, reflections come from the walls and also the ceiling and floor.
If you want to minimise the accoustic mess created by different length reflection paths, use speakers with a minimal number of crossovers and separated drivers. Think point-source, or an approximation of it.
That way the reflections are at least coherent, making it much easier for your ear/brain to hear through to the music.