Hello,
Welcome to Moz, everyone has a different way of doing bits. I'll give you some pointers on what i might do in your position.
First off i'd set up a dev site version of one version of the site - new/old this would enable you to get a comparison of what urls/ content is missing. dont forget its not just urls that affect rankings if they've changed all their content too that will also have an affect. If you want the quick win a restoration may be the most beneficial. I wouldn't bother with 302 to be honest I'd rather put my time into getting it right
Most of the time it's down to how to get a client earning again (assuming it's taking business away) so the quick win here is, restore, set up dev site for new, prep a migration plan. Put into motion.
I'm sure lots of other Moz people will also give some great advice as I said this above is what I may do but as I'm sure you know there is always lots of ways to solve and there is also other subtleties to worry about etc.
The best of luck with your problem.