Just to say, he definitely doesn't qualify as although we are out of catchment now, we were (just) within catchment when we accepted his place. We've since moved house. Technically, it is also walking distance, though not if you are lazy DS.
We also receive the above additional LHA rate in our UC top-up due to their bedroom needs, and also (this might help others) a concurrent council tax rate reduction to compensate for this also. We live in an expensive area so still have to top these things up.
It's really hard, in so many ways, to have disabled DC, but there is some help out there if you know what to get and how. If you receive UC, having a DLA award for your child can also open up qualification for other things; for example, this year, we've received a warm home discount and a cold weather payment. We've never had those before, as we only transferred to UC earlier this year.
I'm glad to see you're feeling better about things OP. It certainly is a punch in the gut the first time you get the award through. It's that confirmation of what you already know, but might have been able to internally ignore for a while, isn't it? << Unmumsnetty hugs to you >>