These sound like great steps, I look forward to hearing what you came up with. It's always nice to get confirmation that acoustic theory met reality. I can tell that your screen and panels were placed so that they visually look right, but relative to the speakers are both too high, which creates these challenges.
As Dave mentioned, you could raise the speakers a bit, and then tilt them down toward the listener. The advantage of that is that you reduce reflections off the ceiling as the carpet is still more absorptive than the floor. I am not a fan of raising the speakers too high. Changing the speaker height does change the soundstage height, regardless of how you tilt them. Tilting them just ensures good even tonality by ensuring you are listening on-axis. For me there is a limit to how high the image should be before it starts to become unrealistic. For me that tends to be roughly at the 1/3 wall height range, but a little higher is ok and even sometimes desirable. 1/2 the wall height is, for me, too high, but some people like that effect. I think it makes the soundstage sound larger than life with music and to some extent, movies.
If you have the ability to take measurements and could share your response, waterfall, and RT60 graph, that would make a world of difference in giving you targeted advice. For example, you ask about bass traps, but I really can't answer that without measurements. I make decisions around adding diffusion or not based on room size and evenness of the RT60. If you have a rising LF RT60 starting at 400-500hz, then I would suggest a full range bass trap. If you have an RT60 that is flat down to 200hz, but need more absorption below that, I would suggest something range limited. If your overall RT60 is very low already, I would suggest adding diffusion and being very careful about adding more absorption. Where you place it also depends on how the room sounds and certain measurement issues. If you have a higher RT60 value but no real evidence of modal problems, then you need to absorb excess energy, but you don't need to target reflections. That means placing traps around the room generally. If you have evidence of reflection problems like a cancelation in the bass range, then you need a trap on one or both of those walls. The most common reason for a bass trap on the rear wall is to absorb some of the LF energy that is reflecting off the rear wall and causing a cancelation. If you have followed the posts on SBR (Single Bass Array) that highlights the effect in isolation.