Time Machine - "tmutil" syntax to inherit backup set for new drive
I am extremely confused as to what names are what disks and partitions and such in your particular scenario. Therefore I will attempt to provide some guidance on the ‘associatedisk’ verb and how to use it, but I can't say for sure the exact commands to run with the names of your existing disks as I don't know what's what.

The associatedisk verb takes a mount point and a snapshot volume, as you found from the man page. This means if you are backing up a disk named "Macintosh HD" on a computer named "George's MacBook" to a Time Machine backup disk named "Time Machine HD", to reassociate this disk to the backup you would run:

sudo tmutil associatedisk -a "/Volumes/Macintosh HD" \
  "/Volumes/Time Machine HD/Backups.backupdb/George's MacBook/Latest/Macintosh HD"


The -a flag associates all other snapshots of the same volume to the disk. This might be useful as you mention something about ‘Latest’ link being broken — point at a specific date/time and use the flag so that the other snapshot dates are associated too.

Feel free to add to your question with a list of disks, partition names and what their purpose is in your setup and I might be able to provide some specific commands to run.