I just replaced a non-boot drive in my 2008 Mac Pro with an SSD. I cloned the old drive to the new drive using SuperDuper and assigned the new drive's UUID to the old drive's backup (* details in comment to follow). For what's worth, I gave the new drive has a different volume name from the old drive.

The good news: My first Time Machine backup with the new SSD in place amounted to something like 18 MB. Yay! (A full backup would have been in excess of 300 GB).

The not-so-good news: when perusing backups in Time Machine, if I want to see a file revision dating from old drive, I have to select my computer's name and navigate to a date before the drive changeover, then navigate to the old drive and to the desired directory. In other words, if I'm in the Finder in a folder (e.g., "Client Work") on the new drive, and I enter Time Machine, TM shows me only Client Work's post-changeover backups; there is a disconnect between the post- and pre-changeover revisions.

It would be nice to be able to peruse pre- and post-changeover file revisions in one place in Time Machine. Anyone think it's possible to bridge the gap?

Maybe I should have given the new drive the old drive's name?

Maybe it would have made more sense to give the new drive the old drive's name and UUID instead of changing the backup's UUID?