I was able to resolve this issue and hence sharing here
Disable Calendar sync in AT&T920 WP8 GDR3 (i don't think GDR2 or GDR3 matters here) to verify that CALDAV is indeed the issue. When I did this the memory errors (8007000E) went away.
Steps I took:
1. I used Microsoft Outlook and Google Apps Sync to get a Local copy of my Google Calendar Data
2. Outlook reported that I had ~26000 KB in my "Calendar"
3. When I sorted the data based on date of entry, I realized that I had VERY OLD i.e. before GMAIL even existed
4. I deleted some old event data using Outlook +Sync.
5. Re-checking, the size of the "Calendar" folder as reported by Outlook was slightly down to ~24000 KB
6. On my 920, I 'enabled' Calendar Sync, and voila ! memory problems went away
I was able to use "Google" account for my email and Contact AND "Exchange/ActiveSyn" for the Calendar
1. Go to Emails/Accounts - Assuming you already have Gmail setup via CarDAV, CALDAV etc. with address firstname.lastname@example.org
2. Add Account
3. Select 'advanced setup'
4. Input any arbitrary name that is different from 1. above for e.g. email@example.com, add password
5. Click Next and choose 'Exchange ActiveSync'
6. On this screen. continue to use the email address as in step 4. However, for User Name enter your Google Calendar ID - For most people this is = your email address i.e. same as step 1. i.e. firstname.lastname@example.org
7. Leave domain as blank, enter the server as www.google.com
8. Uncheck, Email, Contacts etc.
DONE! Now you should have Email + Contacts via the "Google Setup" and Calendar via "ActiveSync"
WHY bother with this and not use ActiveSync for emails also?
This is because there is this huge bug with ActiveSync and Google for mail. If you have a subject line that is >60 characters and you try to reply to the email, the message gets jumbled/corrupted/unreadable
See this Link
I hope this helps people to fix things for some