Congratulations!
I recommend you check out the Metzer Farm blog
http://blog.metzerfarms.com/blog/?Tag=Goose+Feed There's some good information (and a calculator) regarding waterfowl feed. Flockraiser doesn't have any animal proteins. Their website says that they went to that in response to customers' requests. Those requests were a direct result of concern overproviding a more natural diet and the potential connenction between animal proteins and BSE (Mad Cow) disease. Their natural diet is grass. I also feed mine alfalfa, which is pretty high calcium and protein as hay goes, not for that reason, but because the alternative is coastal bermuda, which is, in my opinion, very poor. Geese don't care for alfalfa, but mine are fed that from the beginning, so they'll eat it. You are up where you have a wide variety of hays or grasses that will grow.
I use Flockraiser as the base for my feed, too, but I don't like that the trade-off is that there is no protein from whey or fish. Your main concern isn't so much the source of the protein, but the ratio of protein. Flockraiser is 20%. Layena is only 16%. Game bird feed is high. (Around 30%?) That's awfully high. Adult geese don't need that high a protein ration. Why does the person you got yours from feed game bird food? There may be a very good reason for it, especially in winter. You might ask the question. If it is a seasonal ration, what does that person transition to during laying and mating season, and then again, for adult maintenance. Excess protein fed unnecessarily will turn to fat, and obesity isn't good for their health or fertility.
Goslings require a higher ration of protein, but only for the first 2 weeks or so. I cut back to about 16% as soon as they start developing feathers on their legs. We did not do this with our first babies. We didn't know. We wound up with one of the Toulouse developing angel wings. She is now a pet and she does not pass this on to her offspring. We did it to her, no question. It is not genetic.
The next year we had one start to twist. We were feeding Flockraiser crumbles, but even that 20% was too much. We backed the protein to 16% just in time. We got the little one fixed, but it happened because we were just about finished with the bag and it was the last hatch. We didn't want to waste it, but we dumped it as soon as we saw that start. Flockraiser is supposed to be a "complete" feed. What that actually means is that is meets the basic nutritional needs for a variety of backyard birds of different species. And that makes it not really complete for any of those birds specifically. Many of us don't have access to feed developed soley for geese or waterfowl, so we use what we can get. Last year, no problems, but we cut back as soon as they really start feathering out, and before their wing feathers start.
I mix Flockraiser with other feeds and use layena pellets toward laying season. Mine are on about 16-18% protein, depending on the season and activity level. The Book of Geese by David Holderread also has very good information on raising geese and their nutritional requirements. It's the only book I've found that was written specifically on geese. It's a valuable book to have on hand, too!