Base for Sognefjord and Borgund Stave Church?

The Sogneford is quite large, but traveling so far off-season, your best bet--assuming you don't plan to rent a car--might be to follow at least part of the Norway in a Nutshell path. Be aware, however, that the various parts of that five-leg journey from Oslo to Bergen do not run as often off-season. You'll need to be careful as you schedule things. Scenic trains, boats and buses are not worthwhile in the dark, and traveling in the fjord area isn't cheap.

Flam is the most convenient place to stay, I think, though the town itself isn't particularly scenic. I don't know whether all the local lodgings remain open through the winter.

During mid-summer there's a direct bus to the church. At other times I think the best you can hope for is a bus-bus connection followed by a significant walk (maybe 30 minutes?) with just enough time to see the church and take a quick look at the little museum--but only if your second bus is on time, which mine was not. Keep in mind that in addition to the significant walk to the church you'll be waiting outdoors three times as you complete the round trip. In Norway. In November.

How do you plan to travel on to Tromso?

My idea was to backtrack to the airport, fly on to Tromsø, and then spend 5 or 6 nights doing killer whale watching, dog sledding, and Aurora light hunting.

That should work since you're willing to spend at least one night in the Sognefjord area. However, you might also check on flights from Bergen to Tromso. If they exist and are priced comparably to Oslo-Tromso flights, I'd consider completing the Nutshell route by going on to Bergen. Once you're in the Flam area, especially if you take the Flam-Gudfangen ferry in order to see the Naeroyfjord, you are a lot closer to Bergen than to Oslo.

Ok that makes sense. I only have 12 nights basically to work with. The idea was like 3 nights in Oslo, 3-4 in Flam (excellent idea, thank you!), and then 5-6 nights in Tromsø. I don’t necessarily need all 4 nights in Flam which makes it easy to play with travel time to get to Tromsø.

The town of Voss (last stop on the Nutshell route before you hop on a train to Bergen) is known as a center for active sports. It's not on a fjord and isn't especially attractive. It's also relatively close to Bergen, so I don't know that it makes sense as a place to spend one or more nights. However, it might be useful to have an additional option in fjord country.

I'm a bit concerned that you might run into several days in a row of weather not conducive to outdoor activities--but I suppose if you're planning arctic activities in Tromso, you won't be much bothered by what I'd consider bad weather.