Fran - this is a tough one. From an employer's perspective, the sooner you bring it up the better. If they hold prejudices, then maybe you wouldn't want to work there?
One idea you could try is to go through a third party recruiter. Explain your situation to the recruiter right from the beginning. Recruiters are expert at dealing with these types of situations.
Another idea might be to try contracting or temping first. Once they see how good you are it will be easier for them to accept the negative background check. You could suggest this when you go to interview for a job. Maybe even call the company that gave you 3 interviews and suggest it to them?
A 3rd idea - when you bring up the negative - be prepared. Maybe you can get a few letters of recommendation or references you can give to the employer at the interview which show that you would be a good hire. Nip any apprehension in the bud.
And finally, you might consult a professional career counselor - who may tell you that my off the cuff ideas are bad!
Good luck in your job search!