When I glue them back together, I do them right on the stock using the screws to line the pieces up and the wood surface to do the same. Even flat faced plates are not always the perfect flat that a smooth table top gluing surface will provide. Small irregularities on the back of the plate especially the hard rubber ones fit the wood surface perfectly. Something you loose when gluing back together off the stock.
Curved plates,,there's no better way than to use the orig stock contour.

I do use a single layer of Handi-Wrap plastic over the wood/under the plate in the glued area to avoid it sticking to the wood. It pulls right off the repair afterwards.
MAke sure the stuff is pulled tight w/ no wrinkles in it when you place the plate down or the imperfections may show at the edges however slight.

Sometimes I use super glue to repair. It works well but is not a gap filler for missing pieces.
Any tiny hairline fractures after the initial repair is done can be further filled however by carefull application of a few drops of the stuff and quickly sanding the area.
The sanding dust from the base matl fill the voids along with the glue and hardens almost immedietly.
Use black wet-or-dry paper for the sanding the black hard rubber plates, Most anything else will leave different colored specks in the dust from the grit paper.

I use epoxy dyed black for heavier repairs and missing pieces.
I've never done the repair inserting a small reinforcement in the break as described. But I will do that next time. A good solid repair technique.

Horn plates I almost strictly repair with a super glue. The natural material bonds extremely well with it,,just like your skin and fingernails.
The delaminations along the edges of many of the horn plates I simply douse with the glue and it weeps and draws deep into the layers of material bonding and reinforcing them.
Cracks the same. You can further cover any hairline cracks as above.
Larger missing repair pieces can be made from epoxy, coloring as needed and mixing or swirling a lighter or darker color thru it before it sets to match the surrounding material.
Horn usually gives you a chance to match up pretty well as it usually has some color variance in it to play off of unlike the hard rubber plates.