800-364-4263 Arkansas Game and Fish, they're not open till Monday. Canada Geese are covered under the migratory bird act and it's illegal to keep wild caught geese. You need something that shows it's not wild caught or they'll make a stink and fine you. Just call and ask anonymously what permit...
Just do your best. Remember, without you they wouldn't have any chance at all. Even left with their parents nothing goes perfectly. You're doing a great job. Incubating goose eggs isn't for the faint of heart. That last week seems to take forever.
It sounds like you may not be turning them often enough. Goose eggs should be turned minimum 5-7 times a day and always a odd number. As long as the little one is still moving around I'd try not to worry too much. So much is out of our hands while their still inside those darn shells. It's nerve...