Shimano SPD pedals have generally about 6 degrees of float. Actually, the platform idea is a good one. You can even get the platform pedals with the little spikes, and use the marks they leave in your shoes as a key to aligning the cleats. That will help with toe-in/out issues.
As someone else commented, you may have "vertical out-of-plane" issues as well. Observe how your left knee moves while pedaling, does it go pretty much straight up and down, or does it move left & right as well? Is you lower leg vertical, or does it lean in or out? wedges uner the pedal cleats can help correct for either problem.
Finally, are you mashing with your left leg? It seems odd, but if your mechanics are otherwise OK, you may be using you left leg more heavily, whcih could lead to left knee pain. This is more likely if you are left-handed or a "forced right hander" (naturally left dominant, but taught to write and do other things right-handed).