Yeah, you dun gon messed up!
First of all, simply moving the files themselves is not recommended as the paths get broken for the referenced artwork / waveforms. This is why we suggest using the library > backup and library > restore processes, or migrating to an external drive, in order to move to a new computer.
I'm not sure what you did in order to lose the database after "restoring" it to the first computer.
Yes, your Time Machine should be able to recover your database to a point before your first migration. Start by rolling back to see if that resolves the issue.