It may just be the Line6, but I don’t know, either way. The link I gave you up above is the final fine-tuning of the sweep range. You should be targeting the Manual parameter with expression, and also selecting Manual for the Shape parameter.
It will be easier if you use the Wah or Bass Wah as a Type. Depth & Q-Intensity (resonance) at maximum; Bottom at minimum. You can always adjust those down (or up) later on. In this use case, Speed doesn’t matter. For now, zero out all of the secondary controls (Depth Mod, Speed Mod, Mod Rate, Mod Source).
Depth (Bottom) and Manual targeting / the Parameter Mapping range seem to be the most critical adjustments for your issue. I would think you need to dial the Start up from 0 there.
What bothers me (from your OP description) is the ‘jumps’ seem similar to the Line6 acting like a volume pedal. But I’d like to think that’s not the case here.
