Haven't time to read all this, but I've been there. Agree with the people who say 'go for the area you get most support'. It's pointless living in a fairly affluent area if you won't feel at home.
You could always do what I did, of course:
(kind of wrong, but not really)
When pregnant, I put a large jumper on and went to an independent estate agent in the area I wanted to rent in. Told them I was self employed and needed two bedrooms as one was for an office. Didn't tell them ANYTHING about the HB. I got a reference from my accountant who knew my business was closing, but omitted that bit, just testified that I had been earning x for 'x' amount of time. That seemed good enough for the agents, combined with references from previous landlords. I had an overdraft facility with my bank that I used to make sure I had all the cash they wanted to move in.
You can afford to be more confident. At the end of the day, as long as the rent is paid in full, on time, then they will have absolutely no reason to query it. They've got plenty of houses on their books with paid working people who are lazy with the rent or who lose their jobs. Get some references in writing, and approach independent landlords/agents. Tell them you're self-employed (kind of true), so no paycheques to show. Just get something in writing to prove you've been a good tenant in the past. They just want the rent in.
Hold your head high, lovie. You're being responsible in raising 3 future tax payers.