Does anyone know if there is a way to play the game, as of the OpenDev ending? Will there be another one before launch or is there an early access mode I can play in the meantime?

Negative on the early access.  Unlikely on another OpenDev.  I think that there just isn't enough time to take feedback from an OpenDev and make changes on it before the August release date.  If they tried to have one in late June, it would still only leave them with 5-6 weeks to rewrite the code based on feedback from the OpenDev.  I wish they would have another, but I'm not holding my breath.

Hope to get the 250 turn gameplay... I seem it on streamer

Yeah I wish they could just not close the Victor and play that until release