But the studios probably would not outright dismiss the case either. They would still be prudent to seek an injunction so that Peters couldn't simply create another entity or sell his script or the production to someone else. The studios will also want Peters to certify under oath that he's actually dismantled his operation (similar to what happened in the Carol Publishing case).
The injunction is going to happen come what may I suspect. If Peters then shuts down (and complies with the injunction) then I would have thought the order you refer to could be sought without the need for a full trial and instead by way of an interim application - assuming Peters was agreeable to such an undertaking, which he presumably would be if he shut everything down. The interim injunction would already have stopped him carrying out any further infringement from the date it was granted.
I suppose if he shut everything down but failed to agree to give an undertaking in respect future infringement then the studio would be forced to continue the proceedings until such an order was achieved at the very least. I don't think this is a realistic scenario though if Peters goes to the trouble of shutting the whole thing down while bound by an injunction. Well, not unless he's a bloody fool, ignores legal advice and is in denial as to why he'd being forced to shut down.
Oh, I agree this isn't getting as far as trial should there be an injunction. I was thinking this would be like Carol Publishing, where the parties would negotiate a stipulated judgment and submit it to the judge.
Now, the other thing is that should the judge grant an injunction, Peters could appeal that up to the Ninth Circuit. That will drag things out for awhile, and it would give him a chance to muster up some public support from outside interest groups.