Thank you for the advice. I’ll look into Capone museums.Is there a respected Al Capone museum? Whichever one has the most of his memorabilia. You could send them some good photos, and a list of the names. Maybe they could at least give some sources to start with.
Another starting point would be whoever could match the names to Alcatraz records. Surely they still exist. It's a shame a lot of them are just nicknames, but you've got enough good ones to find in records. The dates are a 3 year span, '36 to '38, there couldn't have been that many different inmates in that time.
If someone made you an offer, I wouldn't jump at it.