Ok, I finally figured out the solution to my wifi problem! My solution above did not work - I'll try to edit that post. I have a TP-Link Archer C5 router. The 5ghz band on it has always worked fine. I've only ever had to use the 2.4ghz band with this phone (it can't see 5ghz networks), and it was a problem with that band, not the phone. It seems that the problem had to do with the router switching channels and widths automatically. Some just wouldn't work or would work very poorly. I changed the router settings to only use the 20mhz width (not 40), and to only use channel 11 (you can pick whatever channel seems less cluttered to you - try Wifi Analyzer app). I now have a great connection on my 650 thoughout my house - the way it should work.
If this is not the real solution I'll edit this post, but I am very confident with the drastically improved results so far.
(I'm not sure that both the channel and width settings had to be switched from auto. It may just be one or the other but I didn't try to isolate the problem any further.)
EDIT: 9/19/2016 I don't think this solution works. I now just keep my router on all the default settings and I still have occasional issues. But the news today is that we're soon getting new firmware with wifi fixes! Hopefully that will help.