Core Data now provides NSIncremental store, which lets you use any web API as your persistent data store. It's possible to roll your own alternative to iCloud in this way, if you choose.
Dropbox does not come close as alternative. Dropbox as of now is file-based sync. Core Data iCloud sync is trying to sync an always opened SQLite3 database file, they do it through database log files. Possible alternatives are TouchDB, Simperium, Firebase but then you have to change your app from not using Core Data. Or rewrite your app to use file based storage as what 1password did. The key is offline sync. File based cloud sync is solved problem. So maybe the way to go is persistent store of client app has to use files.
Edit: regarding offline sync (which I didn't address) something like AFIncremental store is a good example of how a local persistent store can be maintained in tandem with the online store.
(But, as you say, non- trivial and hard to get right.)
https://github.com/stackmob/stackmob-ios-sdk/blob/master/Cor...
And once you discover that you can't fix all the problems that Apple is struggling with, you have dug yourself into a VERY deep hole :)