I've used many Triumphs over the years with little problems once the primary problem was corrected. The tip is glued to the pad with contact cement. The problem with contact cement is if you get it to hot it becomes soft. The remedy that I came up with was that I would glue on the oversize tip as normal but before I would trim to size I would burnish the tip. This would make the glue become soft so that I could easily work the tip off the pad. I would then roll the glue off of the tip or the pad, which ever that it happened to stay on and then, after sanding the back of the tip and the ferrule, I would re-glue as normal and turn to fit. End of problem and the tip would feel more firmally attached to the pad.
You used to be able to get these in 15 mm which was just not wider but also they used a thicker piece of leather which really played much better. They came 40 to a box just like the 15mm LePro's but I don't believe they make them anymore as I haven't seen them advertised for some time.
Dick