... might try just shifting both bindings towards the heel side a bit. Not necessarilly suggesting this as a long term solution, but something that might help give you the feel for better heel side turns (although likely at the expense of the toe side turns). Also, too much forward lean on the boots when they are across the board can sometimes mess up the heel side turns (gets the board too steep too quick and your weight can't get down low enough so you just skid or chatter out or the board tries to toss you over).
Also, putting your board on and just standing around and hopping a bit on a carpeted floor can tell you quite a bit. Should be able to get in something approximating your general riding stance, close your eyes, hop 8-10 times (not a lot, just get the whole board off of the floor), open your eyes and still be REAL close to the same place you started. Any sideways shifting or rotation is a fairly good indication that your set-up could be off and that you are fighting something that could be adjusted better. The sideways shifting seems to be generally due to not having your weight (in a natural stance) centered on the long axis of the board, and the rotation seems to have to do with the angles of your feet/hips and how things twist as you absorb the impact. Pretty much want to take it in the knees and hip joints without rotating the hips and throwing things off. Might need to change the front binding angle, back binding angle, or the difference in the angles, you will just have to experiment a bit. All of this should be also be comfortable, if you are straining anything or working hard to keep the board in line, something is likely out of adjustment.
Final thought is to take the adjustment tools with you so you can put the bindings back the way you had time in case any of this makes things worse!