Hi fine,
When i am having issues with base surface and target mapping, i sometimes solve it by creating a copy of my target object, then dicing and seperating a piece to be the base, then using the edit frame flat snap to get the base ready for the flow. The thing to watch for doing that is too much "fold over or bunching" when flattening the taget into a base.

I'm not in a position to demonstrate or play along right now...