Pix of your glue procedure

[TonyinNYC]

Well.... technically, you can do that with hide glue. Apply the glue to the part, allow it to mostly dry, then use a steamer to reactivate the glue when you have the brace in place. I wouldn't do it, but you could if you wanted to. I know a guy who put a top on like that.
But yes, the fantasy product you speak of would be great.
I think applying glue takes experience. First, I did not have any idea of how much to use, but I knew I wanted enough so the joint was not starved for glue. This resulted in a lot of squeeze out, but I was fine cleaning it. Now I put much less glue and I have less cleaning to do as a result. But that darn bridge....it still confounds me!

[Kevin in California]

I'm late to the party here, but on the bridge gluing........
I have found that I want to see some glue squeeze out around the bridge and I wipe the bulk of it away with a cotton t-shirt rag immediately, then follow with a lightly damped t-shirt rag and wipe away the balance. When I've tried to "chisel" it way with a spruce chisel it is hard to not mark the lacquer and using this technique, all the evidence of glue is gone. Don't use too much water though that it will creep under the bridge and water down your glue.

Kevin

[Dennis in Anola]

I prefer to mask along the edges of the braces and also the pencils line I draw on the top when gluing braces. I apply glue to both surfaces and spread it quickly & evenly with a cheap acid brush. The squeezed out glue can be easily cleaned off when wet using the aformentioned straw method. When the tape is removed you have a perfect joint strength-wise with no further clean up. I also build model airplanes very neatly with epoxy using this method.

[Ken Hundley]

One of the best little tools I have found is to cut a straw off at an angle, then use it to scoop up the squeeze out, either right away, or just as it is skinning. As the end plugs, cut it again a little ways up. Works great.