My opinion, an overstay is rather a minor offense, if you did not commit other crimes/felonies and was just an overstay, such as a few weeks. I do believe that with the help of an immigration lawyer, you could have the US immigration courts reviewing the issuance of a crew visa for employment purpose reasons. Obviously, it might take time and some expenses.
xxx
Remember, a crew visa (sometimes called a shore pass) is quite a limited visa, with limits of the distance where the holder can travel, and is limited on rather short periods of stay on the US territory (is it 2 weeks...?).
xxx
Present valid reasons, employment hardship etc. and request a review of the case, it might be overturned for crew visa only. I understand that his/her ineligibility might still stand for another tourist visa for a few years, but not for issuance of the crew visa. And stick with US Immigration Laws from now on...!
xxx
One flight attendant (Argentina) I know, got problems with US immigration law because she was de facto "living" with her US boyfriend in Ft.Lauderdale. Until 2002, Argentina was a country listed for I-94 tourist visa waiver, but she ran into a problem (I do not recall the circumstances), her crew visa got stamped "cancelled" then later was reinstated. I know she dealt with an immigration lawyer for assistance. She is now married to her former boyfriend and holds a "green card"... and never has problems in Miami with immigration, when landing as crewmember on the GD or as passenger.
xxx
One advice - When frequently visiting the USA, either as crewmember, and at times as tourist visitor on I-94, be sure to have a copy of the GD or the I-94 you used to enter inside your passport, and to relinquish the stub when you leave. One thing I know, if you arrive on the GD, you must leave on the GD, and if arriving as tourist/passenger, make the nature of your stay clear to the immigration officer on your arrival.
xxx
Good luck to you -
Happy contrails