>My main system resides in the great room of our open-concept house - essentially a 30x30 open area (entryway, family room, dining room, kitchen) with 15' ceilings.
Modal issues dominate the bass region for nearly all systems and with identical length+width which are an even multiple of height yours are going to be worse than most.
I doubt you'll be able to solve your bass problems without multiple sub-woofers (where placement will fill in some of the nulls and average out the peaks) and/or bass traps (which will reduce the size of peaks and nulls).
The Earl Geddes/Duke LeJune multi-sub reference given by Jdombrow is a fine starting point.
Modal issues dominate the bass region for nearly all systems and with identical length+width which are an even multiple of height yours are going to be worse than most.
I doubt you'll be able to solve your bass problems without multiple sub-woofers (where placement will fill in some of the nulls and average out the peaks) and/or bass traps (which will reduce the size of peaks and nulls).
The Earl Geddes/Duke LeJune multi-sub reference given by Jdombrow is a fine starting point.