You might want to try running that as a 2D simplification, since these are both revolved parts. It would keep them both locked vertically on the central axis, and you should just need a force on the top "edge" and a fixture on the bottom "edge".
vash, use a prescribed displacement to push where you're showing the force (this will result in your output being the force required) and restrain the other 2 directions so that it goes straight downwards.
fix the bottom component on the bottom to start.
add the appropriate no penetration contact set between the 2 components so that they interact.
patricks 2d suggestion is a good one.
Thank you both, Patrick and Jared. I will attempt both methods.