I would like to suggest a long-shot for the next BUFC manager - Andy Preece.
He knows this league from his time at Worcester City, which he took from 18th in the Conference North when he joined to an 8th place finish. He led Worcester to two further top 10 finishes. Preece also guided them to the 2nd round of the FA cup.
He also enjoyed a successful time at cash-strapped Northwich Victoria, which included another FA cup run, Northwich beat Charlton Athletic in the first round.
Preece has had both a long playing and coaching career, so he may have a few useful contacts, has done well at clubs with small budgets and fits the 'northern manager' tag that gets mentioned on here. Unfortunately he doesn't seem to be on Twitter so I can't 'tap him up' about the job like one or two others seem to have done with Rob Scott, Dave Frecklington and Curtis Woodhouse.