I have a half-cylinder that has been scaled in edit mode three times on the Y axis. It has a Solidify modifier with its thickness set to .7870 (arbitrary, but it shows my problem nicely). Even with Even Thickness enabled, the Solidify modifier does not handle the top of the cylinder very well:
When I try to cut a hole in the solidified cylinder with a cube and a Boolean modifier, depending on where I place the cube, sometimes all the geometry of the cylinder disappears (I didn't hide the cube here; there's really nothing left of the cylinder.),
sometimes it acts like I used Union instead of Difference (and it inverts part of the normals...),
and sometimes it even cuts a hole kind of like I wanted, although it still does a very poor job.
Inspecting the inside of the cylinder, I can see that the geometry of the cylinder is intersecting itself, and that is what I don't know how to fix. Here's my .blend file.
Edit: here's a screenshot of the actual model (side view):