You will be pleased to know that 1Password for Teams does not use Dropbox for syncing and has what we call Better Than Two-Factor™ through the use of an Account Key. From our "Understanding the Account Key" article (https://support.1password.com/account-key/):
With traditional two-factor authentication, an existing device is used to authorize a new one. But the existing device is only used for authorization. The one-time passwords are not used to harden the encryption.
Your Account Key works in much the same way. It is required to authorize a new device. However, your Account Key is actually used to improve the encryption of your data. Both your Master Password and your Account Key are required to decrypt your data.
With traditional two-factor authentication, an existing device is used to authorize a new one. But the existing device is only used for authorization. The one-time passwords are not used to harden the encryption.
Your Account Key works in much the same way. It is required to authorize a new device. However, your Account Key is actually used to improve the encryption of your data. Both your Master Password and your Account Key are required to decrypt your data.
More in that article. :)