For geese, I would recommend Flock Raiser first, but Start&Grow will certainly suffice and would be the product of choice if your geese tend to get too fat. As for going a month without eggs, ChickenCanoe is correct that it could have been due to any number of reasons (though a month oud be a very short molt). Stress is likely, and if this occurred during the heat of summer, heat stress would be very likely. When it is hot and humid, hens tend to eat less, sometimes a lot less, and this will negatively impact egg production, sometimes bringing it to a complete halt for a while. A simple lack of calcium would at first manifest as weak egg shells and then maybe no egg shell -- just the shell-less egg.
Yes, it is sometimes very difficult to feed males separately, and even if you offer Flock Raiser and supplemental oyster shell, there are no guarantees that the roo or drake isn't also eating the oyster shell.