Plastic binding and CA glue?

I just glued up some plastic binding on my baritone ukulele Kit build. I used the Stewmac Bind-All glue which has a 2 minute set time. The plastic binding was long enough to go around the whole instrument. I did not think in two minutes I could apply the glue, set the binding and tape it in place, so I tried to do it in sections. This was a disaster. The plastic binding is installed but there is glue everywhere.

I just watched Robert O'Brien's Luthier Tips du Jour Mailbag 6 - Bindings with CA glue. He tapes up his binding and then applies a thin CA glue between the tape. This way you can be sure everything is perfect before the glue comes out. This sure seems like a better way of doing it.

My questions
1. Will CA glue stick to the plastic binding?
2. It there a better glue then the Stewmac Bind-All glue? It's kind of runny and using a better glue bottle would be helpful.

Thanks as always

My ultimate answer for plastic binding was thick CA glue. Often I'd have three or more lengths going at once, a purfling strip beneath the binding and another on the show side of the top. I'd work in 4"-6" sections. It's important to have a supply of small lengths of scrap wood (usually pieces of binding) to spread the glue after squeezing it out, as well as a supply of masking tape strips ready to go. I like working with Duco cement, too, but the work must remain taped up at least over night due to the way the glue softens the plastic. The super glue can be untaped in an hour or less.