There’s a little tool that will help to seat the rubber stems. It has a cap on one end that screws on to the end of the new valve stem after you’ve put it through the wheel, and then that cap is hinged on a longish metal stick. Use the stick as a lever to pull the stem through to its fully seated and installed position.

Or, as another commenter said, get a stem that fastens in with a nut. You might want to put a dab of blue threadlocker on the nut before tightening it down to keep it from coming loose. This will make it hard to remove later, but not impossible. If you do end up needing to remove it later for some reason, heat it up with a torch first to melt the threadlocker if it gives you trouble. (This will probably ruin the valve core, so take that out first.)