I am VERY happy to report that the inbox on my laptop and smartphone are now in sync. Even SENT mail from my android is showing. I have decided to delete the original account from my Android and just use the Exchange account.
And this setup is SO MUCH MORE RESPONSIVE than what I had at GoDaddy. I would wait for 30-60 seconds sometimes as it thought about moving something for me. No moving email between folders is INSTANT!!
Thanks so much for your help with this!!