IMO, you aren't asking too much at all. I'd be PO'd if my horse wasn't getting outside every day as well, but I'm a stickler for that.
Keep in mind also that I've paid $800+ per month for worse boarding services, the price does not always determine quality.
If you are willing to move (sounds like you are) then if you need to move to a more expensive place, ask if there's chores or things you can do to reduce your board. I ride late, I'm usually the last boarder there, so I do night feed once a week to bring my board bill down, for example. Lots of places will be willing to work with you on that. But if they aren't then maybe you do need to find a way to make the extra cash to pay for the extra $100 a month, which is only $25 a week. I have friends who do sell Arbonne or Fifth Avenue and make decent revenue doing that. The ones who put a lot of time into it, actually live off the income!
They say money doesn't buy happiness -- well happiness doesn't buy horses!