You could certainly try a slightly harder reed to see if it helps. If you want help breaking the habit, I walked through my double lip exercise here for my students who experience that biting issue:

https://youtu.be/PeRMN6TYnT4

When I am biting, I definitely get a bit sore after playing a lot of altissimo. However, it's possible to make not biting a habit too and to make it less of an ordeal. Doing some double lip work up there with a tuner helped me. I have a tendency to be too intense with my embouchure and I do better when I focus on the air instead.