As you noted, thick curtains would help reduce high frequency reflections. The curtains, however, will not help with mid and low frequencies. It may be that the high frequency reflections are what you notice the most now, but when the high frequency reflections get reduced, you may discover that you have other issues going on in the low and mid frequencies. I suspect that you do in a room like that.
One thought is to consider broadband absorption panels, like the GIK Acoustics 244. The idea of broadband absorption is that it is absorping a very large range of frequencies, with the idea of smoothing out the frequency range in the room. Any room has peaks and dips at certain frequencies just based on physics and room dimensions (and it sounds like you have lots of extra reflections going on). The 244s can be hung on the wall, but they also make stands to place them on which may make more sense if three of the walls are sliding doors (that is, so you can move them when you need to).
I was amazed out how much the GIK 244s did for the sound in my room -- for example, I realized I was not hearing all the notes (bass notes, as well as higher frequency notes), voice became much clearer and focused, and everything sounded more natural.
The folks at GIK Acoustics are very helpful and you can email them room dimensions and pictures and get a free recommendation. There are other companies that sell similar products, but I mention GIK because I had a very good experience with them, their prices are very reasonable, and I received very good service.
Depending on how the sliding doors work, you may also consider broadband absorption/bass trapping in the corners. The post above mentions triangles in the corner. You can also do something like a GIK Tri-Trap. Also, if you like the idea of do it yourself, the Gearslutz forcum (under bass trapping, room acoustics) has lots of info on DIY corner traps and other DIY room treatments.