My horse developed the habit of leaning on the bit when he had a cough- I felt bad not letting out the rein when he tried to stretch his neck down to cough, but giving him the rein taught him that he could just lean on me, even after the cough was gone. My trainer recommended riding in a Dr. Bristol (looks very similar to the French link, but has the center link rotated so that the edge, not the flat side, lays against the horse's tongue) to break the habit. I only rode in it during one lesson and saw a big improvement. It's definitely not something you should ride in all the time, but great to have in your tack box to use when it's needed.
A loose ring discourages a horse grabbing the bit, but they can still lean on it if determined to do so. So, switching to a loose ring probably won't fix the problem in itself, but might keep it from coming back if you can fix it first.