I can't be of much help on the specifics because we home ed and so I don't pay quite so much attention to what is happening at individual schools. However, I can tell you that since this thread was last active, the population increase has hit Oxford city schools particularly hard. Many families are being presented with offers of school places which are just unworkable for them, for example being too far away or placing siblings at different schools.
Are you sure you can't be persuaded to consider a nearby town or village where the school situation will be better? Some have a great bus service into Oxford, so you could get into Oxford frequently.
Alternatively, bear in mind that with Oxford's very mobile population, there is often a good chance of getting into the school you want if you are prepared to wait for it. Many parents who don't get their children into their preferred school by the start of Reception will send them to a different school. Then, when someone moves away and a place at the preferred school comes up after a few months or a year, they don't want to unsettle their child from their existing school in order to take the place up. That means that even if you are not high on the waiting list, others above you may decide not to take the place. If you keep your child at preschool or else home educate then you'll be ready and willing to grab a place whenever it comes up. This strategy won't always work, especially with the few ultra-popular schools, but may be worth considering.
I see increasing numbers of people at the home ed groups who are home educating temporarily while waiting for a school place. And Oxford is awash with home educating families, so there is no shortage of things to do while you wait!