Can only say: There was a thread over a year ago with no solution: https://forum.cardano.org/t/exodus-wallet-byron-era-question/126040
Don’t know if the private key would have helped. Probably also a proprietary format and none of the other wallet apps supports importing it. They only support importing seed phrases and if Exodus did something else with the seed phrase than everybody else, then there is no way out.
Only hope would be that you get them to tell you exactly how they derived Byron keys and addresses from seed phrases five years ago. Then, you or someone you really trust could try to redo that to send the ADA to a new wallet.