There are a few ways you could go:

• Local TKLBAM dump and rsync across to new server
• Exclude data (the ~200GB) and just use TKLBAM (either local data dump or cloud) to transfer the main config, then rsync data across
• Configure some local server for your backups (excluding data or not)
• Something else, e.g. cloud backup for base server with local backup for data, etc.

TKLBAM is quite versatile. Whilst is easiest used either automatically via the cloud, or manually via local data dump, it's open source and can be configured to be used with a ton of different backends (not just the Hub). The TKLBAM docs and FAQshould help with the details of that, but I'll note an overview of my first couple of points to give you a head start.

To do a local data dump is as simple as this:

mkdir /tklbam-dump
tklbam-backup --dump=/tklbam-dump

Then rsync the /tklbam-dump dir to your new server and restore on that like this (assuming you rsync to the same dir on the other server):

tklbam-restore /tklbam-dump

If you wish to use option 2, then excluding a directory from a backup is easy, just add it as an override. See the tklbam-backup man page for details, but assuming the ~200GB of stored files are in /srv/storage, then you can add them all (recursively) like this:

echo "-/srv/storage" >> /etc/tklbam/overrides

I hope that helps get you going. If you have further questions, or any issues, please post and I'll respond ASAP.