Take this as you will - feel free to ignore...
How much do you want to fly? Is flying a passion for you or is being an airline pilot what drives you? (These are not necessarily the same things).
If you potentially have difficulty getting an airline job because of youthful indiscretions but have a real passion for flying, have you thought much about other domestic based non-airline flying jobs?
I believe if you *really* want a job flying because you love flying and are willing to look further than airlines or similar and can do it tough for a few years, there are potential options. Certainly less well paying and less glamorous (at least from the outside) and that require a lot of persistence to get but how much do you want to fly for a living?
One obvious example (assuming your previous record is not really a representation of your nature), people with dedication and persistence, good people skills, life experience, a thoughtful attitude to flying (and a passion for it) can make great instructors. Not lucrative in any way (and that is an issue - little money can make marriages and family raising hard) but good instructors are gold (even if they are not paid much gold). It can be very fulfilling as well.
If you went that route my gut feeling would be to be up front about your past to employers and show (with strong references, clean recent record, community participation etc) how your past is not representative of how you are now. Better they find out from you than discover it themselves and think you have hidden it.