Eligibility for specific needs social housing

This is a real problem for you.   One way to get yourself the home you want, where you want, is to look on the private rental market, which will probably mean you have to reduce your standard of living when paying the true value of rent,  because usually, H.B. needs some degree of top up contribution from the tenant.   

 Another way is to live more cheaply and pleasantly by going into a private flat share with people you get on well with.   Your council with thousands of homeless people on the list has chosen to offer you a move, but not to the type of home you would select?  You assume,(and you  know your own area, so you are probably right)
, that the sort of neighbours you have on one council estate will be exactly as hostile and criminal on the other council estate.  You are not realistically likely to get the council to give you some high quality home in a nicer area, away from fellow council tenants and with more rooms than a single person can ask for.   

(Also, given the unmet housing need, with entire homeless families crammed into dangerous and sub standard one room hostels,  sometimes for years on end, it could be suggested that your terrible troubles with mental health and victimisation and persecution by undesirables would not appear to the council to take first priority.   Many of those in hostels have endured the same thing, and have the extra problem that, for instance, they and their children are not safe in their room, not safe going in and out of the building, and not safe to go to the shared bathroom facilities. )

The third option could actually be pleasant, but again it would need you to do some research and be flexible and adaptable.   There are people who need two things you might have to offer them.   A little extra income, and a little extra company.  Nice, decent people sometimes have spare rooms they are willing to let to lodgers.   After what you have gone through, you might feel far better  with a landlady/landlord, than living entirely alone.  The key to your own flat left you all alone when those horrible people did those things.   Sometimes, a flat of your own is not all that much of a prize.   I'm taking it for granted that you yourself are not like them, antisocial and nasty and impossible to live with.  It does seem likely you are right, you need to get away from that sort of neighbours.   Maybe radical solutions are called for.   (Mind you, some people are truly experimental, and live in cars or vans or sheds or all sorts.  Presumably, that way, they keep the local Housing Allowance as extra income?  I don't know how that works, do you?).