Last academic year I raised similar points with Lambeth, suggesting they work towards a joint test with Wandsworth and Southwark, perhaps using the banding element of the Wandsworth test as a basis. They claimed it was cheaper to administer multiple and very simlar tests to the same children in succesive weeks!
Initially, they said it was the cost of giving the test to children applying to a non-testing school (as in wandsworth), but I kept pointing out that that was not necessary - they can just not sit the test. Eventually , they said the cost issue was that they had nothing to kick the process off with, but that Lambeth Academy would now use the main Lambeth test - which is great. They said the getting boroughs and then heads and govs to cooperate over this will be time consuming and cost money.
So I agree that it could be worth pursuing but be prepared for a lot of nonsense to come your way.
Last year, the children I know who sat Dunraven (main Lambeth Test) and Kingsdale (main Southwark test - used last year by all testing schools apart from the Harris ones) said the Lambeth NVR was the same as the Kingsdale test (ie NVR component of Lambeth same as Southwark), which makes the whole situation even more...words fail me.
Last year, Kingsdale definitely was involved in the admission process: it made waiting list offers by telephone and held the waiting list (although confusingly the LA did too and it was never clear whether the lists were identical).
Although it would be great if the Harris academies came into line, that is only the tip of the iceberg: where I live, with a shortage of local places at half-way popular schools, children can very reasonably sit different tests in four boroughs, and for different schools within that.
I would support a campaign to resolve this issue, and I know other parents would locally, but I would guess from previous things I have been involved in that there wil be a time-consuming and frustrating.
However, I don't think it should be beyond the wit of government that for schools allowed to select on academics, it comes up with a short menu of tests (one lot for banding, one for selective), and schools have to pick from them and share the results so that children do not have to keep sitting the same or similar tests.
Problem is: it sounds remarkably like the 11-plus and banding schools certainly, and local and national govt, will not want that association - they prefer to pretend it is not happening.