First off, you mention staying a "day or two on your own"". Denali Park requires at least 3. So unless you are planning on adding more days, you do not have enough time.
With only your stated timeframe, I only suggest you consider Seward. Plenty to see and do, If your cruise sails from there, great, IF not, then rent a costly one way Avis car with a drop in Whittier. There is much more to "cost" to consider than money. In a short timeframe such as what you state- it is definately a waste of valuable time to back track for hours to save a few bucks. How much is your overall vacation worth??
For further clairfication- many people just do not realize the vast distances of Alaska. To consider the Alaska RR, I always recommend an extra day over driving to Denali park. For me, it is a long slow boring ride with trees and more trees via rail. McKinley is seldom seen, which is a highlight. The train also misses everything in between, and so do buses. A rental car is superior, if an option to consider.
Another point is in reference to the above poster's Denali Park "tour". I never recommend the "tours"' and definately will always state that the Natural History tour, which the above poster took is an extremely poor choice. Like going to Disneyland and never getting out of the parking lot.
I just can never understand why it's even offered. Denali Park is a highlight of many Alaska visits. But you have to get IN to the Park. You don't see it from a lodge or the Parks Highway. My min. distance in is Eielson via the shuttle bus, 1/3 the cost of the tour buses. Do your homework and find out the differences, then make an informed choice based on your touring priority. It's unfortunate that some people book tours in Alaska having no clue what they purchased, there are some significant points that can really enhance a trip there.