I've done something on the scale you are trying to do it. From my experience it would be best IMHO to rent a car and stay in hotels or cabins.
You will do lots of driving. Seward would take 3 days by itself (day cruises, fishing, general sightseeing). It would take all day to drive from Seward to Homer if you take your time to stop and see anything. Then another day to drive to Anchorage. That's 5 days and you haven't explored Homer or anything between there and Anchorage. Anchorage itself is worth at least a day. Second the idea on going to Whittier.
Going north towards Denali is a full day there. A day for a tour in the park. Next day a drive to Talkeetna. A day in Talkeetna, (zip-lining, flightseeing, etc..). Next day a full day of driving to Seward. A couple days in Seward. Go home.
Lots of driving and the cost goes up to get a dolly to pull the rental car, because you will need one.
Just my 2 cents.