Hello Frank!
I remember having similar experience when I started using super glue about 30 years ago. It takes practice when it comes to applying that stuff and prepping the surfaces to be glued. I'd like to offer some advice - maybe it will help you and others. First, like my dentist told me once - the glue holds the best when it isn't there - funny saying but there's something to it. In case of super glue it's good to have the parts interlock some way before glueing them, so they hold "themselves" in place until the glue dries. Then, the less glue there is in the joint, the faster it polymerizes and the stronger the joint is. Because of that it might be worth a try to wick some glue away from the joint with some tissue - but be careful, when you mix super glue and cotton the mix gets so hot that it might even catch fire.
Second thing, that was a game changer for me was the observation, that the lacquer thinner I was using for styrene glue also makes super glue dry faster and stronger. Since I observed that I'm always moistening the surfaces to be glued with lacquer thinner. At least this cleans those surfeces, but I have a feeling that there's also some kind of favorable chemical reaction. My lacquer thiner has xylene and butyl acetate in it.
I hope it helps you - good luck with your builds and have a nice day
Paweł