They're different leagues. Shame on your captain for not making sure he had both lineups covered in case that exact scenario happened.
I've had to deal with that before as captain. Players just have to make a choice, I won't put a player in both lineups and "hope" they can make both matches.
If I was in a tight spot and had to overlap lineups, I would have had email correspondence from the opposing captain agreeing to a later start time. Then you could send that to ALTA instead of them telling you to pound sand.