I was told by a Triumph "guru", many years back, when I changed my patent plate, that the old rivets can be carefully driven in until they bottom and that the new ones can be ground down a bit, then tapped in over the old ones. I didn't have to do it, fortunately, but it might be worth a try. They should tap in fairly easily. The "guru" is still doing the classic Triumph scene and is very well respected.
Just the $.02 worth of the "village idiot": Jim
The older I get, the faster I was....until lately!! (Speed IS the fountain of youth)!