If you are flexible on the color/style, you might want to look for molding with a thicker spine. I actually ran into the opposite problem recently on an older CP I was re-purposing and just muddled through it, shaving out the slot and forcing where necessary. But I really wanted to use the 3/4" chrome-stripe t-molding I had available and it has a wider spine. It would probably fit the slot you have just fine.
The only thing I can think to do, other than the obvious glue solution, might be to cut some sections of tape of an appropriate thickness to give you a good bite, and wrap those small pieces over the spine every couple of inches to help keep it in place. It might be cleaner and more reversible than the hot melt, which is difficult to make look uniform.