There are some excellent suggestions on this thread. However I wanted to make a comment for those who, like the OP, "really, /really/ don't want any sort of generic touristy trip," and especially those who are contemplating using FF awards to Alaska.

I'm pretty sure that in most cases, any mileage redemption plan that allows the use of Alaska Airlines (AS) will permit one or more stopovers in any round-trip or open-jaw itinerary. AS redemptions will automatically allow a SEA stopover if the routing is via SEA; and I'm pretty sure they'll also allow a stopover in ANC if your destination (i.e. turnaround point) is past ANC. AA allows a stopover at a "natural connection point" which would most likely be ANC in many cases.

I mention this because, good as they are, the standard tourist loops of Anchorage-Denali-Kenai Peninsula (maybe -Prince William Sound and/or -Fairbanks) are very limiting in that they have to stick with the road system.

But in Alaska the road system barely moves the needle in terms of the area made accessible, or climate/ecological zones penetrated, or proximity to native communities. And although the skies are spacious and the vistas impressive along, e.g., the Denali park road, they can't hold a candle to the experience gained flying over the tundra or the Alaska Range, or seeing the Arctic Slope or the Bering Sea or the coast around Kodiak Island, and so on and so on.

On the road system you can't experience the solitude of a lake in the Kenai Moose Range after the charter floatplane operator has dropped you off for a fly-in fishing trip (one or two nights) at a cabin (with boat) alongside the lake, with nothing but loons, moose, eagles and other beasties for company, until they come back to pick you up - even though you're all of 30 min. from Lake Hood in Anchorage.

Of course not everyone has the time or usually the money for this sort of experience, but some do, and in the case of FT readers, maybe it's not as hard as one would think.

For example, take the OP's week. Day 1, Anchorage; day 2 to Denali; day 3 in Denali; day 4, back through Anchorage to Seward; day 5, AM Seward, back to ANC PM; day 6, fly to Nome/Kotzebue/Barrow; day 7, back to ANC and red-eye home. ANC would just be a stopover on a home-OTZ/OME/BRW-home round trip, usually for the same miles as home-ANC-home.

This is just a suggestion - Alaska has enormous diversity that matches its size, but you need to get off the road to see some of it.