Forgive yourself & your dog too. You live, you learn, and often learn the hard way. I bet your post will save the life of many other geese, reminding us all to be more careful. Thank you for sharing.
I still don't know what would be best for your goose. If you weren't intending to breed you may be able to get another female to keep your goose company. Or she might be content with a duck for a friend, I don't know. I hope some other goose experts will chime in.
I have 2 Pekin ducks, both female I hope, who spend a lot of time ranging with our Embden pair. My kids claim these birds have formed a special White Webfoot Society and consider themselves superior to all the other birds in the yard.
Check in the Where am I/Where are you? section to find folks in your state/county/city/area. Maybe there's someone nearby who has a goose or gander to sell or give away.