Ah, OK, you're right. I got misled because in my iPad settings, it says "myaddress@gmail.com" and underneath that it says "Contacts"... but in fact, it's not a Gmail account -- it's an Exchange account.
I had set it up such a long time ago I forgot how I originally did it.
So, Exchange works fine for me for syncing Gmail contacts. What
didn't work fine (and I confused that with Exchange), was syncing contacts via
iCloud -- so I disabled Contacts syncing via iCloud.
As to CardDAV, this is the first time I hear anything like that is available -- probably because, like I said, I've been syncing Google Contacts using the Exchange way for years, and CardDAV seems to be a recent addition. And because Exchange seems to work OK for me, I have no reason to switch to CardDAV.
Anyway, syncing Gmail contacts should work reliably for you using either the CardDAV or Exchange way. Good luck.
