I'm not a pro with this, but I've worked with a couple Happ Comp sticks and the IL competition stick when building custom joysticks.
In my experience, the sticks should go through that piece relatively easily. At most, they might need a little pressure and a twist. If it's taking more than that, it would strike me that something was wrong.
Are you using the spacer (95-0194)?
With my IL version of the comp stick, when I used the spacer, the very tip of the stick only made it down so that it was flush with the bottom of the actuator (I think that's what it's called). So, for that one, I had to put a little pressure back on the actuator in order to get the C-clip in there.
But if you're not even getting flush with the bottom, I'd be suspicious that something is up. You can pretty easily remove the screws (43-0139) to get at that plastic piece and take a look to see if there's a burr or something in there that it's getting stuck on. If you, you might be able to file it off with a small round file.
Good luck.