I lived in South East Alaska for the last twenty years. It is a very large state with varied climate zones. For the trip up via the Al-Can I suggest late May or early June. There will be years that you will not see good weather but for SE Alaska the more stabile weather is then. The interior can be good through August but SE Alaska is well into Fall with horizontal rain in August. If you want to tour for a month and see a lot of the State, June into July. I know a lot of people will chime in with their experiences, but based on a twenty year average, that is my suggestion.
P.S. If you are thinking of riding one way and ferrying the other, make your reservations early and try to get a cabin reserved.