I still don't see the benefits of 1Password from a cost perspective, regardless of a trust perspective.
I can spend $40-80 and buy a bunch of 1Password license packages, or I can use KeePass and place the database in my Dropbox folder. Yes, 1Password has a more aesthetic interface, but otherwise it basically does the exact same thing.
IMO, the big question is: Who do you trust more when it comes to cryptography and security engineering? The 1Password developers or the KeePass developers?
I use Dropbox, but my password for Dropbox itself is stored inside 1Password. The escape hatch is that the 1Password sync folder is shared publicly, and the URL is copied to a slip of paper in my wallet.
Because I only have one computer and no mobile devices— therefore I only have one copy of the password database, and I need the password database to access Dropbox.
The sync folder is encrypted—is there some risk I'm not seeing?
Personally, I don't believe in leaving something like a password database exposed. That's akin to leaving a safe in the street. While someone might not be able to get in right away, why make it easier?
For you, I would just keep a copy elsewhere (friends computer etc.) or just get an additional device (mobile or otherwise).
To add to this all syncing on 1Password is done using 3rd party vendors.
You can use dropbox, iCloud, Google Drive, etc to do the actual syncing of the encrypted files.