I’m glad I know Sarah Blow and she’s got better eyesight than me, apparently  – okay, and a lot more experience with Windows Mobile. She found the problem I had with ActiveSync immediately and pointed me to a setting in the Connection Settings dialog (File | Connection Settings), called This computer is connected to. This was set to “Automatic”, but there’s also an option “The Internet”. I’m not sure why, but changing this option made the whole problem go away at once… not only the part where the corresponding setting was overwritten on the phone, but also the fact that the proxy settings were reconfigured on every connection. Thanks, Sarah!