Ronboco, I don't think your room is hopeless at all, but it is a different sort of puzzle than most of us have. Your room is so atypical that most of us will be hard put to offer any certain guidance about how to proceed with traditional room treatments in the absence of measurement. I would view your high ceilings as an asset with respect to room modes. Having two large openings in addition to having the high ceilings may make it a challenge to properly pressurize the room. But your room dimensions should give a relatively low Schroeder Frequency, which is that frequency below which room modes predominate, This is very good. It could mean that you will require much less bass trapping than most of us, or said in a different way, you may receive relatively modest benefit from an investment in bass traps and other treatments. REW will help you discern what your room is really doing. In addition to REW, if you are able to connect your computer to your audio system, you can play pure test tones (do a google search) while walking around the room with an SPL meter and find the locations where bass frequencies are being reinforced by in phase reflections and partially cancelled by out of phase reflections. You will be able to discern which of your room surfaces are responsible for particular room modes by noticing if the SPL levels vary while raising or lowering the meter, moving it side to side, and to an extent by moving the meter forward and backwards in the room (mindful the SPL will drop or increase as the meter moves further away from or closer to the meter). This technique could be used along with the crawl technique mentioned earlier to optimize placement of your subs.
I am about 99.9% sure that you would benefit far more by putting 3K into a distributed bass array than putting 3K into bass traps. If I were you, I would move in that direction. But if I were you I'd ask Duke LeJeune the question directly.
Since you already have two REL subs, you should be able to offset some of the cost of a DBA like the Swarm by selling them. If I were to offer advice in the absence of measurement data, that would be my advice.
With your high ceilings, you are not going to be dealing with issues like floor to ceiling slap echo and the room openings will also partially mitigate the side wall to side wall slap echo type problems. You may find yourself in an enviable position where you don't need much traditional room treatment. Time will tell.
Most of us don't want a bunch of bass traps etc in our living rooms if we can help it.