So the lastest thing I tried was this:
Looking at the picture, if I rotate the character movement inward a bit then the tangent becomes a secant of a circle of radius x.
As I change the amount I want the character movement to rotate inward by, I can make the circle the player moves around bigger or smaller. The next challenge would be finding a way to automatically get that value to rotate inward by.
Hopefully, this is a good direction to go in resolving this issue.