I don't know how you keep moose out of the garden. If I had to guess, I'd say an electric fence, because I know they're big.
You might want to think about making a chicken tractor that fits in the space between your raised beds. That will protect your veggies, while allowing the chickens to eat the weeds and till the soil with their scratching. The biggest issue will be overwintering them. Tractors are often hard to overwinter in, if they are too small, not as sturdily built or are low enough to get buried in snow.
You might want to have a smaller, lighter weight tractor that will dock with a larger, more protective coop for winter.
Some people have even built a daytime tractor that will dock with the run on their main coop. You can do it all different ways. I've also had pullets in a tractor during the growing season and then just moved them to the main coop when it was time to get ready for winter. It will depend a bit on how predator proof you want to make your tractor or your garden fence, whether you want to leave them in it overnight.