OK we're back
Jeff, the simplest thing to do at the moment is to use a 16 GB USB stick as the venue for a Timeshift snapshot of Tina.
You would format the stick to Ext4, run Timeshift that is already installed on your Tina, choosing the Location as the USB stick. In your Settings on TS, have the Scedule Tab cleared (no schedule) and the Users Tab set to the right-hand option Include All. This applies to both you as The User and Root if it is there.
This will give you the maximum on-demand snapshot you can get.
Best time to do this is when you are about to effect the move in drives, but don't add too much additional software to the existing Tina before you do so.
13.92 GB so far consumed will likely fit on a 16 GB stick, compression with Timeshift is 1:1, i e nil compression.
If less than 1 GB of free space is available on the USB stick towards the completion of the snapshot process, Timeshift may have a bellyache with either a non-fatal warning or else fail to complete the operation and it will tell you.
I don't have Tina onboard at the moment, but unless it has become bloated over Tessa, install will have consumed maybe 7 to 9 GB, so you have added software is that so?
At the receiving end, that is once the new SSD is in place - if the SSD is the sole drive, you would need to install Tina on it, then use the new Tina's Timeshift to Restore the snapshot from the stick over the top of the new Tina.
If you have a hybrid drive, eg 2 TB SATA with Linux/es on it, and the 1 TB new SSD, you could save on the new install of Tina and just use Timeshift on one of the other Linux to restore the snapshot to the new SSD.
Let me know if this is the sort of thing you want to do, or else specify other.
Friday here in Oz, so