Greetings MOI experts : )
Can I please seek your assistance on a 'simple' solids construction matter.
Please see attached file.

Three profiles - top, side and front. The front / cross section profile should be consistent along the length of the object apart from scaling to a point at the front and scaling in line with the curves at the rear. Note that there is a 'slice' at the rear when viewed from the right, so the side and top profile curves don't meet.

I can't boolean this out of a block as the last bool fails. Understandably as the curves on which ever profile is cut last ends up co-planar with an existing flat surface.
I've tried a sweep, but couldn't quite get the result I wanted.

Any advice would be appreciated!