i think the ‘additive’ option has essentially been useless for a few versions of blender now, as you can no longer bake in additive nla mode (it wasn’t really that useful anyway). but it should still be bumping your original animation untouched as a strip into one step down in the NLA, and then the wiggle bones as a layer on top of it. the idea was to leave flexibility to modify the amount of blending of the wiggle to the original animation after the fact.
if for whatever reason thats not working, or you want to generally have a little more control over the baking process, my bake button is essentially just calling the regular bake action operator anyway. so you should be able to call yourself and set it to overwrite action, which should hopefully provide the desired results!