Having trouble generating a new solid from these two intersecting objects. I believe the problem is that the objects are tangent at the top of the cylinder.
The desired result is attached in white. I was able to achieve it by shifting down the smaller object into the cylinder slightly, but ideally i would like to get the shape without shifting my geometry.
when booleans fail, you can run the intersect tool to generate the intersection curve, inspect it to see where it’s broken and that is the cause of your boolean failure.
IMO, you’ll likely be better served exploding and trimming this surface by surface.