That's beautifully done, Simon. You sure know your way around that tune, which is no piece of cake from the sound of things. You kept it all flowing for the whole duration ... no small feat. Very cool.
Squeaking ... !! We all have to deal with squeaking. It's part and parcel of playing guitar, isn't it. Some moves are just impossible to do without squeaking, and even the best players can't eliminate it. I heard a Joe Pass recording once, him solo on nylon string, and it was one big squeak, really. I used to hate it in recording sessions when the producers wanted all squeaks removed from the part, thank you very much.
It was always the keyboard player producers who made such demands. They just didn't understand.
I guess the only thing to do is to be constantly aware of the problem and to try and reduce it as much as possible. Keeping everything relaxed helps, a conscious effort to lift the hand off the strings more. Like all other aspects of playing an instrument, daily playing and working on the details is what keeps it all progressing ... even just a few minutes per day.
Good playing though, Simon.