Joshua,
I do see your point of wanting to have a separate account for your kits that you created.
You are not able to have two version of the Creative Cloud application manager installed on the computer.
When you sign out of your Educational subscription and sign in with your Typekit Adobe ID, it is a different profile as you know.
Switching back and forth could of caused corrupt data for the Creative Cloud app with signing out as it would remove fonts synced with Typekit.
Removing the OPM.DB file will help reset the CC app manager and you should see your fonts when you log in with your Educational CC subscription.
You can still log in to the Adobe Typekit Webpage with your Gmail Adobe ID, while being logged in to the CC app manager with your Educational subscription. That is thru a web session
When you sign out of the CC app manager for the Educational paid subscription, you deactivate the software session. You would be prompted to sign in to use the software when launched. That is why you are not able to use the software while being signed with your Gmail Adobe ID. It is not associated with the subscription. Can you try adding the fonts that you need from the Gmail ID to the EDU subscription? You should be able to add the kits and have the same fonts for both accounts. I know you mention that you want to keep the accounts separate, as I was thinking that would be less frustrating for you.
Thanks
Scott