How to create a spiral sweep that thins out/tapers at the ends as it intersects with itself.

Hello everyone, I usually work with basic shapes that don't require extensive surface manipulation but I've been stumped over this problem for a good amount of time now.

What I'm trying to make:

A taurus/donut shaped object that gives off the appearance of swiveling on itself to create a pig's tail/spiral motif on both sides. (See sketch).

What I have done:

Created an oval profile sketch for a spiral swept boss/base path; so far it just looks like a slightly twisted taurus. (See sketch).

Doing a compressed helix/spiral with 2 revolutions brings out the shape I desire, but I still can't make the ends elegantly thin out.

I'm assuming there's a way to manipulate/vary the spiral sweep but I can't seem to wrap my head around it. Any help will be greatly appreciated.

SolidworksSurfacing