In my experience, it depends if your child is already there in the indie mainstream school. Or if part 4 of your DC's Statement names that indie school (probably as the result of an Appeal/Tribunal). You have more of a chance if your DC isn't already in the indie school.
As other's have said, it also depends on your LA. And also their relationship with the indie school.
My son was in a mainstream indie and LA wouldn't consider it at all - in fact he was turned down for SA as a matter of principle. As time went by towards my appeal because of refusal to assess, it became very clear that my LA absolutely hated the indie school he went to. I still have no idea why they hated the school so much, but I have some very damming documents as to the LA's feelings towards this school - despite it being Ofsted outstanding for its SEN.
I ended up removing my child from the indie school, home ed'ing him for a year and then Tribunal named an expensive indie SS which now totally supports all his needs.
It would have been tens of thousands of pounds cheaper (yearly) for the LA if they had agreed to my original request - that they only pay for the extra support/therapy/provision needed to keep him at the original indie school. But then my LA has never been logical as far as my DS or his original indie school has been concerned.
OP I fear you will have an uphill battle to get this. Also I vaguely recall seeing some case law that it doesn't matter if you get a staff discount. If the cost of the provision has to be decided by a Tribunal, then the full fees have to be taken into account - not the discounted fees.
I would also question if the school is actually able to support your DS, even with 1:1 support. Some private schools simply are not geared up to provide this kind of support. My DS's old school certainly wasn't able to - despite their Ofsted outstanding. We lurched from term to term with them not knowing what to do and them chucking inappropriate provision at him. It got worse as he went through year 3. It ended up with him getting an anxiety disorder precisely because of their methods and me having to home ed him to stop him having a nervous breakdown at the age of 8. Also thrown into the mix was the fact that after I withdrew him from the indie school, my LA refused to name a state mainstream school he could go to whilst he was assessed for his Statement.
Good luck if you decide to go ahead with it. I hope your experience with the LA and the indie school isn't as appalling as mine was.