I don't know what the specifics looks like. As @Desert Hound mentioned, some deliberate bracketing in a major showcase would likely work and scratch the itch for inter league play. It would be great to see top teams from each league play each other from time to time. Plenty of bragging rights to be had on both sides.It's probably not necessary to have a GA v ECNL tourney because both leagues do not limit the outside tournament competitions their teams can attend. Surf Cup and Albion Cup have GA v. ECNL games. There are probably many tournaments across the country having ECNL v GA games. The southwest is tough for the GAL girls because their competition is not great and they have to travel far for good competition when there are plenty of great teams in their backyard. Maybe southwest GAL can play GAL showcases and more tournaments but use their local leagues to play league games instead of traveling for league games.
I would guess the GAs approach to SOCAL SW is fueled with a little bit of patience. They have a good base (WC, City, Albion). Surf is essentially straddling the fence with SDSC in the GA. It will take time. Population of CA is big enough to fuel two leagues. Migration will occur. Not enough to challenge the likes of Surf, Beach, Legends, LAFC, etc, but enough to provide a level of competition that is acceptable to parents and is useful to college coaches. The GA leadership team is plenty experienced. I'm sure their goal isn't to topple ECNL in CA, it's to become a respected alternative/option for the athlete population that isn't in ECNL. Some of that talent should/could be in ECNL but aren't for many reasons.
I don't know who would argue that the best teams in CA aren't in ECNL. That's a given, especially this year. Youth soccer is tribal, I get it. It's in the best interest of the leagues for parents to be tribal.