Well, I just wanted to check back in and say that my HTC One is humming right along now that I have turned off PowerSave Mode. Since that has been off I haven't noticed any issues with this flicker on a white background.
Also, I should note here that HTC Support has been very nice and helpful. I think I am just going to email them back and say I am good to go.
Hope this helps someone else out who may have been experiencing this issue. It's a great phone.
- Johnny Fever.