Have you considered using a Toursaver coupon? Check with the hotels before buying the coupon book, but I think they have both Kennicott Glacier Lodge and Ma Johnson's Hotel in McCarthy in the book. Reduces your cost quite a bit. I assume the Currant Ridge Cabins in McCarthy are on the side of the bridge where the McCarthy Road is, so not quite as convenient as the other two options I mentioned above. The hikes are mostly in Kennicott so if that is important to be near the trailheads, opt for that. It is a $5 or so one-way shuttle ride from McCarthy to Kennicott.
I would think you can fly in if you stay at the cabins. The airstrip is in McCarthy then probably get the shuttle to the bridge and have the cabins meet you at the bridge (or walk from the bridge). I don't think the shuttle runs much after 5-6pm, but I can't imagine they would stop the shuttle before the last flight into McCarthy.