I don't believe anyone here has recommended the very first thing you should have tried and it's not clear from your statement "placed left speaker on the right and right speaker on the left and vice versa" whether you did this properly :
DO NOT SWAP ANYTHING - leave all cables, all settings, - EVERYTHING - exactly as it is when the problem is most pronounced.
Now just physically move (swap) the L and R speakers into each other's place - again, with all cables, wires, EVERYTHING! still attached.
If the imaging problem has not switched sides - then it is something in the room - PERIOD! CASE CLOSED! It cannot possibly be in the equipment. And you have already had your hearing tested. You can start experimenting with how to "equalize" the room better.
If the imaging problem HAS shifted to the other side - then it is something in your equipment - PERIOD! CASE CLOSED!
This is the only experiment that needs to be done to determine if it's a room or equipment issue.
If it IS the room - keep in mind that just because the dimensions are symmetrical does not mean that the resonances of the walls and floors (determined by construction of the house) are symmetrical. Is one wall an exterior and one an interior, etc.?