In that case, you can look at the modified date first. Better than re-calculating hashes.

I guess the methods I propose will not guarantee proper syncing if for some reason a file has changed but the metadata hasn't...

A hashing/checksumming filesystem would make it possible to determine whether a file's contents have changed without reading the file. The burden of computing the checksum is then shifted to writing, which in theory occurs once per sync in the case of Dropbox. This burden is merely computational, rather than a complete disk I/O burden imposed by hashing the file when Dropbox restarts.