Kit Darby and his Air, Inc. company used to have a service that allowed you to purchase a background check to be performed on yourself by a private investigation firm. The investigation firm acted as if they were interested in hiring you for a flying position, and would then send out the appropriate release forms so that any records on file would be discovered. All the information they collected was then compiled in a packet, and sent for you to review as the true "customer".
I don't know if that's still available from any company today, or how to go about contracting with an investigation firm that is familiar with airline hiring practices and the records that go with it. Check with fltops.com to see if they have anything comparable to it?
Overall, I thought it was worth it. I had decided to go ahead with the background check after I flubbed my first airline interview with Great Lakes. Maybe a little pricey for someone still trying to get their first job at a regional, but it put me completely at ease with answering questions both on future applications and in interview sessions. I had three things I was concerned about: two speeding tickets, and an aircraft incident that was reported to the insurance company. Everything came up clean.