Default [Q] Restore apps from old Google account onto new Google account

Hi,

Background context
I recently migrated from a free Google account to a Google Apps account.
I now have most of my app purchases assigned to old@gmail.com and some recent app purchases assigned to new@gapps.com.
To the best of my knowledge it's not possible to transfer those purchases from old@gmail.com to new@gapps.com.

I'm using a Samsung Galaxy S III (GT-I9305) with CyanogenMod 10.1.3-i9305 and Titanium Backup Pro.

Scenario
I reset my phone and configured it with old@gmail.com.
I downloaded all the apps purchased with this account and performed a backup with Titanium Backup.
I reset my phone again and configure it with new@gapps.com and restore my apps from the backup.
Titanium Backup alerted me that my Android ID had changed, so I reverted back to my previous Android ID.

Problem
When I try to update apps purchased with old@gmail.com, I get a 403 error in Google Play.

Question
Is it possible to update apps via Google Play if they were purchased with a different account and restored onto your phone?