Synology: Time Machine backup keeps stopping without errors
New information has come to light. The Mac may need directory repair, significant space freed or just an erase install based on multiple clean Time Machine starts failing.

It’s hard to pick apart backup issues with such a custom setup.
I recommend you start with the “nurse” procedure at the bottom of my answer - working up to fsck and safe boot as appropriate. Exclude three folders and let a minimal backup complete. Consider throwing away the old backups and starting with a clean slate, no restrictions or fancy settings - let Time Machine think it can use the entire disk.
/Users
/Library
/System

If the interface asks to skip all system files, say yes. Once you have hourly backups going well. Remove things from the exclusion one by one and focus on disk corruption on the source if that’s where the backups hang.
Also, disable cron forcing things while stability is not present. Let the normal triggers work until you’re solid is my advice. Also, The Time Machine Mechanic and Backup Loupe are invaluable tools for me working on problematic Time Machine situations. Yours seems overly not easy, so something is causing you pain that hopefully can be identified and remedied.