I think you are approaching this in a wise fashion. Here is a summary of what I did with the auralex pannels.
After I determined the corners behind the speakers were the main culprets, I bought two 2x4 pannels and glued the pannels to a 2x8 foam inslulation pannel that I bought for $10 at Lowes (Auralex sells the glue for $20/can- Yikes!) I cut that down the middle, giving two 1x8' columns, which I wedged into the corners behind my speakers (Magneplanar 1.6QR's) It actually looks pretty good, since it gives me two tall thin columns flanking the tall thin black maggies. Also, the pannels are removable, since they are wedged into the corners and held in place by friction. I bought some smaller pieces and glued them to the ends facing out to hide the blue foam insulation panel. All of this cost me $95, and it completely removed the problem I was having. I bought some additional pieces that I'm still experimenting with for the back corners and side wall reflections. (If you have someone run a mirror along the side walls while you watch for the areas where you can see the speakers in the mirror. Try some panels in those locations too.
Then I would start with the weakest link approach to your equipment upgrade. If it were me, I'd replace the CD player and interconnects first and see where I was with the sound.
After I determined the corners behind the speakers were the main culprets, I bought two 2x4 pannels and glued the pannels to a 2x8 foam inslulation pannel that I bought for $10 at Lowes (Auralex sells the glue for $20/can- Yikes!) I cut that down the middle, giving two 1x8' columns, which I wedged into the corners behind my speakers (Magneplanar 1.6QR's) It actually looks pretty good, since it gives me two tall thin columns flanking the tall thin black maggies. Also, the pannels are removable, since they are wedged into the corners and held in place by friction. I bought some smaller pieces and glued them to the ends facing out to hide the blue foam insulation panel. All of this cost me $95, and it completely removed the problem I was having. I bought some additional pieces that I'm still experimenting with for the back corners and side wall reflections. (If you have someone run a mirror along the side walls while you watch for the areas where you can see the speakers in the mirror. Try some panels in those locations too.
Then I would start with the weakest link approach to your equipment upgrade. If it were me, I'd replace the CD player and interconnects first and see where I was with the sound.