OK, I sorted this out myself in the end. The glass screen on the front is held down with double-sided adhesive. If you VERY carefully prise around the edge of the screen using something thin enough to get in between the case and the screen (those blue plastic things you get with an iPhone repair kit are ideal, but I used a scalpel blade and lots of care), you can gradually lift the screen off the case.
As expected, the USB connector had some corrosion on it at PCB level, and a bit of IPA and a tooth brush got rid of that, and now I can get it talking to my PC again!
I had to scrape off all the old double sided tape from both the inside face of the screen (use something soft like a plastic scrape or your fingernail here, otherwise you'll remove the black screen background) and the inside of the housing, then put some new double sided tape down and voila - its as good as new!
Not sure how watertight my double-sided adhesive job is, but time will tell