>> What you can do is extrude your curve into a surface (use "both sides" option), then do a "mutual trim".
This is where you select the 2 objects, then do a trim and at the point where it asks you to select cutting objects, just push "Done" there. This signals that those objects are both being cut and acting as a cutter as well.
This will leave you with the pieces, and you can then join those pieces back into solids.

Hey !
Added to my "bag of tricks". I had to experiment a bit to understand what you were saying but after that, the only question was why I could not imagine such an easy and obvious solution earlier by myself ! ;-))

And that's something I like in software like MoI. As a lot of actions can not be done automatically by thousand of dedicated tools, to compensate you really have to figure out how to solve the modeling problems with a more "basic" set of tools. That's part of the fun and of the creative process (as long as you're not working on a deadline). Reminds me Blender some years ago or even Bryce where some really creative guys used terrains (yes, terrains !) to create trees and simulate foliage long before there was a "tree tool"...