Oh, hon... you sound so frustrated and "lost" (I hate how that sounds, but that's how I feel for you). And I understand all of what you're feeling. I do. I wish I knew how to make you feel better about it but I don't.
I DO think that part of his unmotivation is the natural course of "coming home" and why deschooling is always pushed; but I completely understand that you don't have that luxury of time to give to it. I'm just saying this because I'd hate for you to think he's truly unmotivated to learn vs. going through the natural course of what happens to kids that leave PS--ya know? I just think it's too early to really say he's truly unmotivated. Not that it changes anything about the situation, but it may put you a little more at ease to know that this may not really be your child's true nature.
Is there a reason he needs to go back next year? Believe it or not, the math (and other subjects) could be really easy to catch up on once he's in a better frame of mind. I think as parents, we are brainwashed to panic about these kinds of delays--and in your case, the idea of going back next year is only compounding that and adding pressure. Is there a reason he can't continue to homeschool?
Frankly, I pulled my son during the pre-K year when he was already reading at a 2nd grade comprehension and *I* panicked my way through the deschooling year. I had no clue that a 4yo would go through such a thing coming out of a preschool. I was also a former teacher and a project manager before that... can you say "planner" and "control issues"? I felt pretty certain that it wasn't going to work out for us. And a huge part of the problem after the whole deschooling year was trying to reconcile the way I do things vs. the way he learned/learns. And that was NOT. FUN. So you have that on top of all of it.
Can you work with what he WILL do? He likes snowboarding magazines: can you read through the articles and find some kind of educational connections that you can lead him to through talking about the articles? I have to do this with mine and it took me a while to get over the annoyance of having to learn how to get him to learn. But I read the articles and analyzed what I could connect it with so that I could talk to him about stuff he enjoyed and then connect it to something he wouldn't connect it to. I would sneak math up on him through his allowance and saving for things that he wanted (at 13, I think he's at algebra or pre-algebra--so that should still work). Would he possibly want to figure out how much money someone could make selling boards if the materials cost $x, etc...? Especially if it's snuck into a conversation that seems harmless: "I wonder if they actually make any money selling those things?" just to try to get him started. Talk about the different snowboarding trails and what makes the rating different (undoubtedly slope) and if there's some kind of slope factor to each rating. Could he design a course? (don't they have a video game like that somewhere?)
Or is he driven enough to go back that you could lay it out for him and say "Hey--we're moving to a better school district and the kids are going to be at a higher level than the school you left. You're really going to need to do some catch-up work before you go back."...? Mine is 7yo and has said he wants to go to PS (but being 7yo, he sees PS as a place to hang out with his friends all day). The deal has always been that he will need to show me that he can do the schoolwork for his age level in order to go. If he opts not to show me, then he can't go. He's stopped asking. Granted, mine is seven and I don't care if he never goes. It's not exactly the same; but if yours is driven to go, maybe telling him that he needs to step it up will work. And tell him that he's at home with all the time in the world to do it. Frankly, it doesn't take 6 hours/day to learn what it takes the PS to cover in 6 hours/day. When I was teaching I did home instruction and the district (one of the best in the state) said that when working one-on-one, you could cover a week's worth of high school curriculum in 4 hours/week. I went back and looked at my own classes and started to understand how that could be... but the point is that he doesn't have to work all day every day to catch up. Does he realize that? Maybe he envisions learning as sitting at a table for 4-ish hours/day...?
Have you asked him how he plans to go into a new, better middle school next year when he's taken a year off? And obviously if he gets anxious about this, you'd ask him if he'd like some help with getting back on track. :)
Of course, only you know your kid and know whether these approaches would completely backfire and push in the opposite direction. :(
Regardless, hugs. Breathe.