. . .
When I go to restore (enter Time Machine), I am not offered a choice of destination. I can only think that TM uses the 'latest' backup ... which contains one week of past history ... instead of my synology backup (6 months of history).
Correct. It uses the current or most recent backup.
How can I select which backup to use when restoring?
Use the Browse Other Backup Disks option, per Time Machine - Frequently Asked Question #17.
or how can I rebuild my TC backup from my Synology backup, if (when :-( ) it fails again?
Practically, that's often not realistic. If a backup set is intact and passes verification, you can copy it, but it takes a very long time. See FAQ #18. Since both are on a network, you'll need to copy the sparse bundle, per section 2 there.
According to my long discussion with Apple Care, the way to change the current backup set which TM uses is to run a manual backup.
It's odd they didn't mention the Browse... option, as specified in the Help:
Also covered in the blue box of Time Machine - Frequently Asked Question #34.
Message was edited by: Pondini