as Jeremy and Robert said already, you got the 24 hour grace period at airport, no fine, but a little stamp. You will have no problem entering in June.
The Thai Consulate in LA is of no help in such cases. A well connected Immigration Lawyer can help to clarify, unfortunately I can not point you to the correct person. IMO your wife have to do the initial running around and try to get information from people who have done this case and than you try to find the superior in that case. Be careful of people who tell you they can clear Blacklist, it is not possible. To fight the case your wife has to go through court. Blacklist are usually 100 years if going through court, but appeal is after 5 years possible, overstay case can be 5 years. In order to help you a bit you need to clarify that point. You can also send by message the stamp so admin can see and translate.