The part that makes your case a bit difficult is how your profile curve runs up above the ends:




You may need to do something like make the initial surface bowed upwards something like this:



Then since you would not have a solid you'd need to build the cutting surface as an extrusion and use Edit > Trim to trim each of those surfaces with one another instead of using the booleans.

There is another sort of shortcut way to go about it as well which might be easier for this particular case, which is to cut your top open ellipse edge into 2 pieces using Edit > Trim with the "Add trim points" option, then when you have 2 pieces use Construct > Loft to build a lofted surface between them. The resulting surface will be compressed down into single points at either end but it will probably be ok. If you want to post the 3DM model file for your object that you have the screenshots of in your first post I can show you how to do that on your existing model.

- Michael