Aw, set them already!

The cantle plate rivets are pretty easy. The Brooks Pro has solid copper rivets, while the Ideale 80 has semi-tubular rivets (except for the one on top of the nose, which is solid copper). The two have to be handled differently. With the semi-tubular ones, I'd place the saddle upside down on an anvil* with the rivet head flush against the surface of the anvil, then pound down on the cantle plate with a hammer and punch very close to the rivet, but not on the rivet. You should see the underside of the rivet, which is a splayed star shape, come up a bit. Then punch the arms of the star down a little to hold them in the new location. With the solid copper rivets, the whole rivet has been compressed and there's no way it will move through the cantle plate; so you have to work from the top. Place the cantle plate on the anvil and tap down the edges of the copper rivets with lots of little blows. If your anvil has a corner sharp enough, place the underside of the rivet right on the corner so the anvil supports the rivet, not the cantle plate. If you can do that, you can hit the rivet head as hard as you want, and compress the whole thing.

The nose rivets are not so easy, because they cannot be supported from the underside. Still place the thing on the anvil as firmly as possible, and tap tap tap. You probably can't make it perfect, but you can make it better.

*For an anvil, a cutoff piece of an I-beam girder is a good option. Or maybe a bar bell weight, or the head of a sledge hammer. Or embed an axe into a chopping block and use the back of the axe head as an anvil. Another option is to slam a pickaxe deep into the ground so one of the points is sticking straight up; place the underside of the rivet against that, and tap on the head with a hammer.