Hey Hank, I read your introduction
so I kinda get what's going on. First I want to be absolutely sure that your problem is the phone itself and not your accounts.
Can you confirm that this ONLY happens while the phone is on? If something was mining your personal data for your credentials, they may be using them without the need for a phone.
If your phone is not rooted and you have performed a hard reset (did you do this through settings or the recovery menu?) there really shouldn't be any residual malware lurking about, unless you have reinstalled the offending app.
As El Presidente asked, we'll need more specific information to help you out, but here are some general observations.
If your phone is rooted and you have installed something into /system, without knowing specifically where it is, a factory reset will not remove it. What you will most likely need to do is to reflash the stock firmware, which essentially replaces every file on your device with a clean copy. To be absolutely sure, you will want to reformat the internal storage partition on your phone as well. If I am not mistaken, that's a 3 GB partition on the Blaze? If you have an external MicroSD card that you suspect is compromised, you may want to format that as well, which is done from the phone menu>settings>storage.
Let us know what we can do to help.