I understand the issue which I think most others here haven’t. The added weight to the joystick is causing his stick to flick the opposite direction when moving from a desired directional input to default position (with thumb off the stick because they are using the thumb to jump).

I think this isn’t an issue you can really get around if you keep your setup that way and your sticks are not stiffer. The only solution here is:

Get a controller with more tension in the sticks (maybe yours is older and looser?)

Or

Play bumper jumper or claw (or get a controller with paddles) so you never have to take your finger off the right thumbstick.