I don't know about the Galaxy Tab, but when I had that happen on my Nexus 5, the thing that worked was deleting my Gmail account and then adding it back in. Same as you described, I went through and make sure that synching was enabled, turned the phone on and off, etc. Nothing helped. So I deleted that email account, turned the phone off. Turned it back on and then added the gmail account again (as though it were brand new). This also opened all of the screens for determining what synching I wanted, etc. Not the most convenient solution, I know, but it worked for me.
Good luck!