You have made sure that all Google Play services are completely up to date correct? I know you said you uninstalled and reinstalled the Google Play store but I just wanted to double-check about the services.
For some reason the site isn't letting me reply to your most recent question... But I had uninstalled all the updates on just the google play store. No changes to play services.
I also tried the malware app that was suggested to me and it found no issues.
Give this a try: clear cache and data for the Google Play services, Google Play Store, and Google Services Framework? Then go into your accounts and sign out of your Google Account, then restart the phone and re-sign into the Google account.
This website isn't letting me reply to any messages from page 2 of the thread so I apologize if this is out of order.
Here's where I'm at now. On Sunday morning I did another factory reset. This time I did not re-install any previous settings or apps. Just my contacts and SMS history. The phone worked really well after that. I documented every change I made to the phone and the apps I installed. By the time I went to bed last night, the phone was getting sluggish on downloads again. I went back and deleted the last app I had installed and tried another download and that didn't help. So it seems it's not related to any app I have installed.
I cleared the cache on play store and play services, removed my google account and rebooted then readded. That seemded to work. This morning I tried downloading an app and while they're not installing at the pace they usually do, they're working. It sure seems like the issue is caused by something with my Google account.
Thought I'd provide an update. After working for about 1/2 of the day, the phone has gone back to not installing apps or app updates as well as being very delayed on app notifications. I'm not sure what else there is for me to do with it.