Twitter – Why Allow Dropbox Integration for Following

I haven't used their service, but CloudHQ seems to offer what you need.

From their website about the Basecamp / Dropbox integration:

CloudHQ simplifies management of Google Docs, Basecamp, and Dropbox files Manage all your Dropbox and Basecamp files directly from a Google Docs interface CloudHQ will continuously synchronize Dropbox, Basecamp, and Google Docs CloudHQ can also backup Basecamp projects and Google Docs to Dropbox

You'd need to have a third name as you'll need to do this:

1. rename @mike_me to @somethingrandom
2. rename @mike_and_long_name to @mike_me
3. rename @somethingrandom to @mike_and_long_name

From what I remember when other users have changed their Username your followers will still be following the accounts they were originally. So if @Joe is following @mike_and_long_name and @Bill is following @mike_me once you have completed the swap @Joe will be following @mike_me and @Bill will be following @mike_and_long_name.

It would be sensible to warn your followers that the name swap was about to happen so that they don't unfollow because they now think that they are following the wrong person.