It's always a lot more difficult when specific constraints need to be incorporated into things!

If the outside is meant to be one regularly tapered piece, it can be good to build the bottom edge as a wide ribbon surface (sweep with Twist: Flat can be good for that, seems like you may have already been doing that) something like this:




Then that can be used as a cutting object in boolean difference to slice off the bottom of a longer tapered thin walled base object:




The boolean difference between the thin-walled base solid and the cutting surface will yield 2 divided solids, and the bottom one can be deleted to leave this:




This approach may be good if you're focused more on the bottom surface following a particular centerline path rather than focusing on the final boundary edges of the bottom which in this case come from intersections between the side walls and the cutting ribbon.

Anyway that approach would give more regularity in the outer surface since it would come all from one larger piece. It certainly may not apply if you have other things that are more important than that though...

- Michael