I just shove them in, but that's not
the answer you want. So.....
Why not use the crate to
feed them their tasty foods, like grains or alfalfa? I sort of do this with my sheep. I have a special small run-in pen where they get their goodies. In fact, that's the ONLY spot that they get them, ever. Thus they are all eager to enter the small pen, then exit down the shoot in order to get a tiny handful of grain before exiting. Then whenever I need to work with them, I simply shut the exit gate on the end of the shoot. They all pile down the shoot but can't leave, whereupon I can go down the line to deworm them, trim hooves, or whatever.
In your case, I'd prop the door open and condition them to go into the crate for goodies. Get them use to your walking around the crate, touching their butts, touching the door. Just don't close them in just for the fun of it, because once they are spooked they may not go back for quite a while. Of
course, this conditioning may take several days or several weeks. It's not a quick fix.