Hi, alaskan here. The tires you're on would be okay for almost all of the state-operated gravel airports. They are generally well maintained due to commercial air taxi operations in planes such as bonanzas or navajos. I would stay away from all gravel bars and beaches or unknown surfaces. Sure, there are plenty of gravel bars landable on that tire size, and even some hard packed tidal beaches, but always hard to know until you know.
A wise plan would be to upgrade to the airglas nose fork now or soon. This opens up a wide array of tire size combinations for you. A good size to start in the bigger realm would be 850x6 mains and 700x6 or 800x6 on the nose. This would allow you to land many gravel bars and a few of the nicer beaches reliably. It's not outrageously large either, so not much speed loss and likely you'd never go back to small tires.
If you want to experience more beach landings at the expense of weight and speed, an 850x6 on the nose and a 10" main wheel (850x10 or 29" tire) is what almost all commercial operators run for landing the beaches. It gives a good safety margin on gravel bar or softer strips as well. If you went this route, I would order the wheels/tires from airframes alaska and then pick them up whe you get to Alaska. You could even list them for sale when you're ready to leave if you wanted.
Even with these precautions, it's still a nose wheel plane so be careful and have fun!
Wild Cessna 206's seen grazing in their natural habitat. Both have 850 nose and 29" mains.

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