When I glue top cracks I use hot hide glue and I do it in two sessions. The first with glue only in the crack and the main thing is to keep the two sides of the top level. In session two I add some cleats to make the crack secure.
Today I used the bridge clamps with an added wooden piece on the inside to keep the top level over the cracks. Worked great!
This is how it looks on the outside. Acrylic plates are nice, you can see the crack. I always use plastic wrap on the cauls, the glue will never stick. Before this picture I have poured a lot of hide glue on the top and moved the top around the cracks to get the glue seeping through. Easy to wipe off the excess glue with a damp cloth before clamping.