To test the room-acoustics hypothesis, you could hang quilts or blankets on the walls temporarily to see if tizziness is reduced. I would put them on the sidewalls 1/2 way between speakers and listener.
To test the "source is the problem" hypothesis, you could borrow a good CD player from a friend and see if that improves things.
Likewise with the "amp is the problem" hypothesis, though I doubt that a CJ Premier amp will be causing tizziness. The CJ stuff tends towards the mellow side, in my experience. And your SF Line 2 got a review from Tom Norton saying it doesn’t emphasize or hype things, which to me means it’s not likely the culprit, either.
To test the cables hypothesis, you could buy some returnable cables by mail order. (That would be my last thing to try, but it’s your choice.)