It might be related to your pedaling style. Possibly, you're exerting peak force too early while the knee is still very bent. Delaying the peak push, might make a difference.

On steep climbs, rather than standing, I push farther back in the saddle, which is sort of like raising the saddle and opens the knee a bit. Then, I think steam or hydraulic power, and press smoothly and more lightly, through a longer arc. At first it took conscious effort, but now I do it without any thought as easily as changing gears.