Really cool idea :) I never thought about translating a bullet hell into a board game, and I think this seems like a nice initial concept to make it work. I think the lack of order while playing it might make it a tad confusing for players, though.
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So, the only problem that I saw with it being real-time is, "When do the Mothership 'bullets' hit the Starfighters?" But when I make it turn based the 10 sec timer becomes an issue, as well as when do you purchase upgrades? do you give up an attack or move action or even a whole turn to do it? There are all sorts of action economy problems that open up. I thought with real-time it's just silly chaos.