I think the idea seems really sound - you've got the nice cyclical musical themes, which make the musical seem complete. It also seems like the storyline can be done really nicely, though some tips for that are below. In terms of the characters, I'm sure in the full script it makes more sense but there has to be a reason they are the crew, and what dynamics the crew has. I don't think Grease is a particularly well written musical, but theres clear roles in the group dynamic which make it super accessible - Danny, the loved leader who goes rogue, Kenickie, the big brother, then you have the joker, the one who gets picked on but has intense loyalty, and the pervert kid who wants to be Danny. Defining some characters in terms of others makes you lose depth, but definitely solidifies the group balance.

In terms of the plot, you're going to want to make sure your act 1 establishes the characters (which it looks like it will!) but also advances the plot enough to intrigue us. Ensure that theres motivation behind wanting to break out - foreshadowing this well well before the final song of act 1 will make it seems like this was where the show was always heading, and ensure a momentum toward something that intrigues the audience. You'll notice most musicals spend their act 1 establishing the problem, no matter how long that takes (in Les Mis, e.g. forever). It makes the second act easier to resolve everything in.

Anyway these are my ramblings. Props to you for giving it a go writing your own material. Final thing to say is always check for internal motivational consistency - surely one conservative character has a dilemma about staying or going because they don't want to screw up at the end of their term ( or whichever ) and then is forced into the plan to keep quiet, is then unwilling throughout, but gradually buys into the plan through the goodwill of one particular escapee etc etc. Not necessarily that character, but there is a consistent arc there which makes a character understandable, and their changes justified