Before I reply, my credentials for your inspection are that I'm a teacher (not Maths, admittedly) in an 11-18 school, and I've worked as head of 6th form before switching to head of department. I know a lot, therefore, about the practicalities of A levels and ucas applications.
Op, I understand your disappointment and frustration, but - I mean this kindly - your plan is bonkers. For one, I can't see how you'll have the time to teach him. Most schools offer 10 hours a fortnight of class time per subject, on average, and expect students to match that in their spare time doing homework and private study. You might get through work quicker as a one to one, but you're still going to need a lot of time, which will obviously replace time spent on other subjects.
Next, the "filler" subject. The school won't see it as that. If he doesn't put the effort in and underachieves, that may trigger behaviour contracts, and will in all likelihood negatively affect his ucas reference (and no, you can't choose who writes that). If he fails a subject, he may be forced to re-sit the year or in extremis, leave the school.
Ucas is another problem. You have to inform them of all AS subjects taken, and predicted grades. The school will do this part, so how will Maths be on there if you're not telling them about it?
I would think it highly likely that a Maths exam would be on the same day as another of his subjects.
Finally - every school I've worked in has re-sat pupils every year. I find it unlikely that your son has stayed in middle sets when he should have been in top set. You have a very scornful attitude towards this school; why not send him somewhere else instead for a fresh start?