I know you didn't want to mess with equalization, but with that room and those measurements, I'd look into a DSPeaker Dual Core 2.0. It can help with big humps in particular. Dips can be harder to get rid of with DSP. I love mine. Use it with both my digital and vinyl rigs. DSP for the bass, and then you can manually adjust the EQ elsewhere in order to tweak the sound to your liking. With that glass sliding door, I'd guess you might find you have a little channel imbalance, which the DSPeaker could also adjust.Check out Greene's review in The Absolute Sound.
And Tweek Geek offers these for audition or with a solid return policy. So a risk-free proposition.
That said, I also think that you could also benefit from treatment (though I don't see too much room for it). And how much does WAF need to be taken into account? You're likely stuck with the glass doors, though thicker curtains may help. The plant behind one of your speakers could be replaced by a bass trap. And maybe could something be attached to the closet doors behind your listening position.
If BRM is correct, then looking into treatment for the ceiling could help? Again, WAF will be a concern.
Really not an expert, so just throwing out ideas. Brian Pape at GIK has always been super helpful with my challenging rooms. Hopefully he or someone else from GIK will pipe in soon. But in that room, it may turn out that your options are limited.