If I may, I'd like to offer a "blue sky" proposal. This is a view from within a vacuum, with the benefits and limitations as such. I acknowledge it may not be realistic under current legal constraints, but as DAO has existed for centuries, I don't think some broader thinking beyond our lifetimes would go amiss. This is just some food for thought. It is meant to be considered in its entirety as a single meal. All are welcome to chew on it or spit it out as they please.
1. Wean off the DAO foundation money. The current school as we know it in Potters Bar is a migratory outcome of land use in Islington. And it would not be what it is today without the cash influx from this inner London pipeline. But there comes a point where we need to ask if this is like pouring more sugar into an already sweetened cup of tea. It is still a state funded school, it is not going to starve.
At this point in its history, I think a better use of the foundation money is to make another DAO school. Replicate somewhere else what has been done in Potters Bar. Regardless of whether people agree with the notion of a partially selective school, one cannot deny that there is a demand for it. If it took about 40 years to make the school at Potters Bar into what it is today, why not sprinkle that fairy dust in 40 year cycles to make more DAO schools in the future?
2. Remove the sibling policy. This is a very competitive school to get into. In light of this, a sibling policy is akin to a privileged back door. I think we mentally transfer this idea as an automatic entitlement which comes from a comp bias. But DAO is no comp. If the sibling policy were to be removed, (perhaps not immediately but phased sometime in the future,) I suspect this would still remain a heavily oversubscribed school.
Knowing what the rules are, parents would act in accordance. Test-based families who are still keen would get all their DCs to take the tests. Distance-based families, of which there would be more than currently, would form a spectral range depending on how far from the school they are. Those very close to the school may feel relatively "safe" for younger DCs. Those further away may have to take a view on whether it is worth risking it. If it is essential for all their DCs to attend the same secondary, then don't apply here - go to a normal comp.
If this all seems ruthless, I would say it is not much more than what it already is for first time DCs. The main difference is that it does not reward subsequent complacency.
3. 50/50 test/non-test places. I hang on to the (perhaps fanciful) notion that an ideal split for a partially selective school should be evenly divided between those who got in via test and non-test. I like the "healthy deadlock" principle of neither side being able to be a majority on their own.
There will be those of you who think of this as a naked attempt to officially establish more selective spaces than currently. I wouldn't say this is untrue. But I would also urge you to read the previous posts on this thread to understand what the demographic breakdown of the school actually is - a majority of kids from test-based "selective families". A removal of the sibling rule and a capping of test places at 50% would in fact be a reduction in the number of kids from "selective families" compared to what it is today. And it would do so cleanly and openly.
4. Remove the Islington minimum quota. Even if many of those highly-prepped kids from Islington would've gotten in anyway, this is a blatant preference system that nonetheless rankles. If the school could do the above (- detach itself from the foundation money, remove sibling places, and create a 50:50 split,) there shouldn't be a need to have a separate Islington admissions list. For historic reasons, Islington could be kept in the catchment to take the tests, but simply put on the same level playing field as the other catchment areas. They shouldn't need to get any special treatment above this.
When the school at Potters Bar can fully cut its umbilical cord to the DAO foundation money, it could rename itself something like "Potters Bar Academy (a former DAO school)" or similar. The next DAO-school-in-progress could then don the magic Dame Alice Owen name as it receives the foundation money to help build it up. I would hope such a passing of the baton would act as an antidote to resting on the laurels of the success of the prior.