Second, clip the corners of the starting end of the film.
Careful when doing this. The tip of the film can climb out of the groove and stick into the next winding. Then you have a real problem. The best is to cut the leading edge perfectly flat, and between sprocket holes, not through them. There is no difference in the friction from flat or bevelled corners. The entire film causes the friction, not only the leading tip.
It is not only the reel that must be dry. The film must be perfectly dry, too. So make sure the learners are handling the film with gloves, or at the very least, very dry hands.
Any residual fixer, wetting agent or anything else for that matter will leave a spot that cannot dry. If the reel has been thoroughly washed and dried, it can be lubricated by using the pencil method described earlier. However, I have never needed this myself.
If you are rolling bulk film, be careful about loading too long. Two or three extra frames can make the difference between it fitting or not. But it won't cause a third of the film to stick out.
If after all of this a particular reel gives perennial problems, replace it with a new one. It might have a small crack or scratch that causes the film tip to snag, or something else that might be difficult to see. Or the inside of the groove has become simply too rough from over-use. Whatever the issue, a reel costs less than the time you are going to spend trying to extend its useful life by 10%.
EDIT: One more thing, as someone else mentioned, reverse curl. I never load film directly from the camera into the reel. Most cameras reverse the bend of the film, and it takes a good few hours rewound into the cartridge for the film to rediscover its inward curl. If you partially rewind with the leader sticking out, cut off the part that bends upwards (away from the emulsion side). Otherwise it will cause a lot of extra friction and may be impossible to coax into the reel. The best is a curl that is the same as the reel itself.