I've updated this, going for these boundaries:

Cutteslowe https://www.openstreetmap.org/relation/19756980

Summertown https://www.openstreetmap.org/relation/19756982
Sunnymead remains a quarter, now within Summertown.

North Oxford https://www.openstreetmap.org/relation/19756981
Now including only the proper North Oxford.
Waterside and Trap Grounds, on the West side of the canal, are out of it, for now. Not sure if I should include them.

I'll mark it as resolved, but feel free to reopen if you had comments.