I could be wrong here, but the only way I know of to see a menu of tags is to post first and then use the tag icon on the post. That icon takes you to the page where you can add tags either by filling in or selecting from the menu. As far as I know, there's no way to see a menu from the original "post an entry" page.

That's the way I always do it, and while it is an extra step, it's just a matter of seconds. It doesn't, however, solve the problem of how to get community members to actually do that...

I know there's a way to suggest features to the LJ staff. Maybe a menu option should be suggested, if it's not already in their queue.