Knee issues do not lend themselves to simple logic.
As Thetank suggested, try moving your saddle fore and aft (try aft, first); and, lower/raise your saddle so you still have a slight bend in your knee even with your heel fully down at the pedal's lowest point.
Regarding mashing, we all mash.
Minimize mashing and maximize pulling up by visualizing a "master leg."
During the spin, focus on what just one leg does, either one or alternate, it doesn't matter.
The other leg will mimic the "master leg."
Make your left leg your master leg for awhile and then your right leg for awhile.
Or alternate them every time around.
Your left leg will teach your right leg will teach your left leg will teach your right leg.
When you get out of the saddle, try pulling more than mashing.
Pull yourself up that hill by pulling up on the rising pedal (you will automatically push down on the descending pedal whether you want to do so or not).
Visualize pulling your knee forward as if to hit the handlbars (don't worry, you can't).