How do I treat this awkward space?

[ppadru1]

I have a two-story place, accessible by spiral staircase that leaves a giant gaping hole in the second story. Apart from the small amount of reverb I can hear out of my right ear due to the stairs opening (which I've gotten used to), I dont know how else to better treat this space and maximize the efficiency of my mixing. I was also considering buying some new monitors, but pehaps I should sort out my treatment issue first?

Would it make sense to move my computer where the keyboard is now?

 

[GIK Acoustics]

I wouldn't move to the left, it would likely give you a larger imbalance than the reverb you hear in your right ear.

Otherwise, even though the ceiling has a large angle on it, typical suggestions for treatment would still equally apply. Bass traps in the corners (you could do the angled wall and sidewall corners as well). Treating first reflection points should also help with that reverb to the right (among reducing comb filtering from first reflections). The only different suggestion I would give your room would be to absolutely treat the angled portion above you.

We've got a lot of the basics covered here: Room Acoustics Primer - GIK Acoustics