I dont think its your equipment.
The human knees/body build is meant to face any kind of motion in a forward direction. Clearly running forward is easier and more natural than running backwards, and the same concept applies to skiing.
Skiing backwards is completely harmless but carving backwards is placing lots of stress on your knees while they are already in an unnatural position. When skiing forwards you naturally lean and bend your knees to turn, but skiing backwards you put the stress on your straightened downhill leg in order to turn. The muscles on the sides of your legs are actually pretty weak compared to those on the front/back of them, which is why i think your knees have shifted and your having pain. This is all theoretical, I am not doctor.
The bottom line is do not continue to carve backwards so much, i think its creating more problems for you than its accomplishing.