Below: finished results, from inside the cab, at rear of door. No more holes, just nice new aluminum rivet heads.
In the plastic bag, the rivets as supplied by 3 Brothers Classic Rovers. A box of 3/16" aluminum backing plates were purchased elsewhere, to serve as the metal support plates inside the rubber door seal.
First step, drill a 3/16" hole into the rubber seal from the inside surface, going only through the first two layers (out of three). Don't drill through the outer curved part. Keep the drill turning quickly so that the rubber doesn't bind to the bit.
Secondly, use a pair of needle-nose pliars to slide a backing plate into the hole. The rubber is quite stretchy, and will allow the backing plate in and then essentially close up afterwards.
Third step, center the backing plate within the seal using an awl or whatever serves the purpose. The rubber will keep the backing plate in position once it's where it needs to be.
The next step is done on the Land Rover - just doing it here for illustration. Push the rivet through the hole in the door seal flange on the Land Rover, then through the seal and backing plate. Then the tubular rivet can be squeezed very easily. The rivet squeezer means the pressure on the river can be modulated to be just tight enough to hold the seal, without flattening the inner surface of the seal too much and thus distorting the seal, as usually happens with pop rivets.
That's all! : )