The problem with these costs are that if you have a rogue authority who don't want the school you want, they will play with these figures and say that there's no case law about how they should be applied when comparing costs.
The figure of £10k for the base cost came in last year, and as far as I am aware, there is currently no case law how this £10k should be applied when comparing comparative costs. My barrister attempted to clarify it during my Tribunal last Summer, but because we "won" on need, not on cost, his very lengthy anaylsis on this was not remarked on at all by the Tribunal. I suspect, that this was fortunate for us, because if we had won on cost, then the LA would probably have challenged his analysis and application of the £10k - precisely because there was (still is?) no case law.
However, there is strong case law that the AWPU for your LA per key stage can be used. And that this should always be the starting point (but not the final point IYSWIM) for working out the cost of a school placement.
There has also been new case law (in the last month or so) that when comparing costs, the LA has to include all the costs of a placement. IPSEA's note is on it here
Case law for comparing costs
Whilst this particular case was based on the extra cost of social care, this new case law also covers items such as "bought-in" SALT provision, OT provision etc.
You can also include the cost of transport - which often works well if you say you will cover the transport cost to your preferred school (so zero cost to the LA). The LA will have to pick up the cost to their school. But they might try to zero cost it if a taxi/bus etc is already going from roughly your home to their school. Although if it's a taxi company, the company will often charge to add another person to an existing contract - in which case you can use that additional cost.
I'm sorry. This doesn't answer your original question. But this new case law might help you in other ways?