Couple of comments, a suggestion, but not necessarily any solutions though. 1) Your original post talked about a shift in the highs to the right. I think this is consistent with your description of your room and speaker placement. I'm a bit confused by your now referencing a drift to the left.
2) Use of a solo piano recorded and played back in stereo is not a good test for judging imaging. Usually they are multi miked and in many recordings the engineers have tried to re-create a life size piano (one that spreads over much of the stage between the speakers) and the dominant sound often is left of center, depending on where the recording mikes were placed and how they were mixed.
If you want to see what happens with high frequencies in your room get some recordings of solo instruments, typically reed instruments. They are much more capable of giving you a pin point center image to judge and hopefully balanced reproduction of room acoustics.
A CD/LP which has been of significant help to me in setting up and evaluating music (not test tones) in my rooms is "Depth of Image" by Opus 3. This was originally one of a series of LP's and is now incorporated into some CD's with additional cuts from other CD's such as Timbre. It is minimally miked, small, medium, and large sized groups and vocals of classical and jazz performed by some Sweds. It has been my touchstone for over 25 years regarding timbre and imaging. Each cut is accompanied by a description of what you should hear, and some of the instruments are very revealing of limitations/faults in your system in the high's such as a recorder and an organ but will also show what your system is doing right. A facinating exercise I think.
BTW, you haven't addressed your set up specifically, but don't forget that ceiling reflectons can be as much of a problem as side wall/floor 1st reflection points and are just as much influenced by toe in the effect of which is much overlooked. You haven't (at least I don't recall) ID'd your speakers, but assuming they are cone speakers here is a suggestion for you (one that initially appears counter intuitive) that is often used by professionals in difficult rooms.
Set your speakers up so that the axis of the speakers cross well in front of your listening chair. For example if you are listening in an equal lateral triangle with your speakers pointed straight ahead you have created a 22 1/2 degree angle. Try toeing in your speaker until you have passed your listening position 22 1/2 degrees and then gradually toe it back towards the listener position until it locks in. You will be changing (minimizing) the effect of lst reflection points on the wall, you will also be changing the effects of the reflections from the ceiling and floor. Give it a try before you spend any time or money making panels, drapes, etc. It's FREE. And you can get used to looking at cross-eyed speakers! :-)
