When you ran the DSL Checker, did it correctly return your address exactly the same as the RM database?
Have you spoken to your neighbour to see what service they have?
I think in your position I'd be talking to someone like Zen, who are more likely to pursue this on your behalf rather than the "Computer says no" you're getting from the big names. Assuming they can resolve the issue, you'll maybe pay a little more. But there's no in contract price rises & you'd be free to move to a cheaper supplier after the initial contract expires.
