It would be a risky strategy. There is no guarantee the LA will name the school, especially if it is wholly independent where you will need to show the LA’s proposed school(s) can’t meet DC’s needs &/or it isn’t unreasonable public expenditure. You would be able to appeal, but there’s still no guarantee and it would be extra time you would need to fund the fees. Even if the school is named, there is no guarantee the school would refund the fees, because the LA won’t be under an obligation to fund retrospectively. If the fees would be a real push, you need to make sure the figure quoted includes everything. There are often additional fees for extras/additional support. You also need to think about how DC would potentially cope with 2 moves in quick succession.
If DC can’t attend school full-time, the LA has a duty to ensure they still receive a suitable, full-time education. Have you requested alternative provision?
You mention the LA EP taking months, if the LA isn’t complying with the statutory timescales, you should email the Director of Children’s Services. IPSEA has a model letter you can use. Post back if that doesn’t work.
If you get an independent EP report that can be used if you, the LA, and the report writer agree it is sufficient. If all agree it is, new evidence should not be sought. Although LAs often disagree it is sufficient.
@addies there are schools who cater for academically able DC. If you post where you are, someone may have a suggestion.