Well either I really frightened Groundspeak, or plenty of other people were having the same problem (more likely, the latter), but this issue seems to have been fixed with the release of version 4.0.1 this week. There are about a half dozen improvements listed in the 4.0.1 release notes:
2. I've select a PQ containing 750 caches and am ready to download:
3. A friendly warning screen appears explaining that this action might take some time:
4. I politely ignore the warning and proceed to download:
5. After informing me that the application is unpacking my PQ, it then moves on to saving my PQ; complete with status bar:
6. And, Success!