After having made the suggested changes, I can report no change. I was out and about, and it didn't sync for 1.5 hours. Then I hopped on a wifi network somewhere, and voila, it synced. Mentioning this in case it triggers any insights ;-)
However, at home I'm always on wifi, and there too it hasn't synced at the designated intervals.
Just tried it again at home, sent myself an email, waited 9 minutes, no check/sync. Sync interval in AM is set at 5min.