Troy,
I' m familiar with the same day airborne exception for Kodiak deer. That said, it takes a while to land, park,hunt, shoot, field dress, pack out and load a deer. Most of the beaches there are fairly steep and they go away fast as the tide comes in.
There are some bigger beaches, but none like the Bering Sea side of the peninsula.
And, you have to get your plane to and from Kodiak.....over Shelikof Strait. I've made that trip many times in single engine airplanes, and not a single one of those was fun. That's about forty miles of REALLY cold water, and some of the nastiest weather anywhere.
If you have NO time constraints, that may not be a problem......but bring a generous credit card balance, cause you're apt to spend a lot of time sitting in a hotel waiting.
Again, get airline ticket to and from the island, then make reservations with Andrew Airways or Harvey Flying and go for a flight in a classic Widgeon.
But, if you don't mind long overwater legs to get there and back, and you're willing to dance with tides and weather while hunting, go for it.....it's been done.....just not frequently.
You can give the Kodiak National Wildlife Refuge office, and ask to talk to the pilot. They can give you current info on hunting and perhaps beaches.
MTV