Given how the problem doesn't appear to be with whatever phone you're using nor your Google Contacts list data but rather your lack of a reliable and usable online connection (neither WiFi nor mobile data), I would focus on getting that straightened out first............................
It's not even a matter where you need a high bandwidth connection for something like contacts syncing (it's just some relatively small text data) but it's still an absolute requirement........................
The above two paragraphs appear to be somewhat in contradiction.
Firstly, I did clicked on the Contacts Sync when I had a good WiFi connection.
My (limited) understanding is that Contacts will sync, or they will not.
Your second paragraph seems to allude to that as well.
I am still as mystified as ever over the much celebrated and touted "Google Sync".
All of my experience with it to date, including this last one, have done nothing but reinforce the conclusion explained in my original thread.
Is this a matter of my lack of comprehension?
I certainly don't think so...............but......what do I know?
But..........thanks for coming back to this thread,
Jim.