Q: How can we take the recorded HoA (which shows up inside our Personal Profile's Connected YT account) and Move it Over to a different YouTube account that our 'Business PAGE' has on YouTube? The MP4 download may be an option to download from one YT account and then upload to the other YT account, but the quality of the video seems to be nasty when that is done.
The short answer is that you cannot move a video from one channel to another.
This is how G+ and YT recommend you handle the situation where your YouTube channel and G+ account are linked to different Google accounts.
How can I make a NEW YouTube Account (aka new Google Account) properly for the Business Page I am making?
You can only create one YouTube account per Google account.
Is your YouTube channel using a channel username or your Google+ identity?
I was under the impression that you could be running your Hangouts on Air from your G+ Page, and if you use a YouTube username you can both give your channel your page identity and link your G+ page to it.
(At least my YT channel is linked to a Page rather than my Profile)