I like most of this. Its really a great story idea. Here are my issues...
1. The combat fleet, it sends the wrong message. Its okay to be armed, just not armed to the teeth on a peaceful exploration mission.
2. The destination, would a more logical destination be the next closes galaxy?
I would like to see the ship maybe be more of a mobile space dock, makes more sense for a one way mission. It could be equipped with a trans warp conduit which cannot be setup until the station reaches its destination. Until then they could use it for communication.
Also if this is going to be a decades or centuries long mission, it would be cool if every season jumped a decade so we can see the crew aging and handling the loneliness of transverse the void.