You need to appeal against the school named, and use evidence that the cost to the LA of the placement in special school they want, is no less than the cost of sending him to indie school. If there is a difference in cost (and this is discounting the first £6,000) you have to argue that the placement is not suitable, possibly with professional reports or recent evidence of his needs; in fact the needs outlined in the EHCP and the provision outlined in relation to those needs should show that the Indie school is more suitable.
If the provision is not sufficiently quantified and specified and the EHCP does not make reference to hours or environment or class sizes you can appeal not only against the placement but against Part F (the provision)
Ring up Ipsea, and if necessary email them, they are quite helpful in sending back info by email if you cannot get through on a personal basis. They will explain the legal aspects.
You need to appeal before the time limit on the covering letter with the EHCP. If you can find out what the cost to the LA is of the Special school and transport etc, is it nearer or further than your preferred school for example? Would you be willing to forgo transport in order to save money which could be put towards the fees - another argument you could give to get Indie.
The LA initially refused to pay an extra £5,000 saying it had to come out of the school budget, but combination of appealing and standing our ground and threatening JR in long run meant they gave in before the appeal was even a few days old. I think if you just show the facts/evidence to them and show you mean to pursue the matter they will often come to the conclusion that it is not worth proceeding to Tribunal, but you have to show them you have the facts at your disposal.