slow Google sync - are you noticing that when the phone is awake (screen on), gmail doesn't sync quickly? Or that when phone is idle (lying on a table, screen off), your gmail notifications are delayed?
If the latter, that may be because of doze
So my issues seem to be on my home network. I am using project fi and my work wifi is behaving normally. So the issue is TimeWarner or my Linksys EA7500 router. All other Internet use is fine 80-100mbps. The only apps affected are Google Apps and Candy Crush. Any other thoughts?
Sometimes, for unclear reasons, Google servers don't work well if the router has IPv6 turned on. Log into the router's settings and disable IPv6 temporarily, then see if it works.