Sounds like some great new suggestions for Idea Station.
I manually tried the suggestions presented here and had no problem performing the workflow in Patch space. So at least for now you can complete the workflow. Here is what I did:
While it's a T-Spline, make it not intersect. That solves the intersect problem.

After it's converted to a Patch body, split the handle.

After the handle is split, extend it into the bottle, trim out the bits you don't want, and stitch it all together again.

Shell it and you are done.

The thumb abides.

Found a few things you might notice, so I'm logging bugs on this:
1. Split body seems to extend the cutting plane really far without checking "extend".
2. Cannot intersect the Patch body across itself, which doesn't seem right, hence the need for splitting the handle.
3. Logged improvement to convert T-Splines like this into Patch bodies if possible, linked to Idea Station posts. (you still have to vote 🙂 )
Thanks,
Phil Eichmiller
Software Engineer
Quality Assurance
Autodesk, Inc.