I would get a desktop charger and an extra battery or two.
The fact that the normal wall charger works is proof that you don't have the usb disconnect problem
So the next step is to try to clean the usb port. I poked around with a paperclip and removed some dirt, but that didn't help.
And I guess there's no chance that this could be some software issue? Any way to diagnose that?
My best guess is to find a proper FTP program, upload the files to my net folder and then download them to whatever computer I use. I suppose I could somehow set up file transfer between a (Windows) PC and the phone over WLAN?