How to prepare summer squash without the peel becoming rubbery
So it sounds like you're saying that you prepare the squash by slicing it in half, removing the flesh, leaving just the peel, then you return the flesh back to the empty peel. You then bake this as a whole. You want to make the peel crisp/crunchy but not rubbery.

Because the peel and the flesh have different compositions, (i.e. water content, density, etc.) and you're trying to achieve two distinct textures (tender flesh and crunchy peel) you could consider using two separate cooking techniques, one for the flesh and one for the peel, rather than cooking both together, once both have been cooked then you can reassemble them. You could bake the flesh just as you've been doing because it sounds like you're satisfied with that texture. 


You might need to experiment some with the cooking technique for the peel to achieve your desired texture. One possible solution would be very quickly deep-frying the peel, this should soften it, but allow you to keep it crisp. 
You could also investigate pickling/lacto-fermenting the peel, this would allow you to get a crisp texture, while softening the peel. 
Another interesting option is the use of slaked lime (aka Thai red lime paste, Thai pickling paste, cal, or more accurately as Calcium Hydroxide, see here for more details). It is commonly used in food applications to cross-link the pectins that "cement" the cell walls of fruits and vegetables together, thus it preserves a crisp texture that will stand up to intense cooking methods. This is used in South-East Asian cooked fruit desserts and in pickles.


If you don't wish to cook the peel and the flesh separately, then you could use a two step cooking method, like first baking them with the cut-side facing up, then once you've achieved the desired flesh texture, flipping them over and quickly broiling them. The broiling will affect the peel significantly more than the flesh in this approach because you will have flipped them so that the peel now faces up and is closer to the broiler (which provides intense, top-only heat).