Hi Brad,
Here are a couple things to think about;
June is SE AK tends to be the drier of the three summer months, although weeks of rain can be encountered any time of the year. On the other hand, August is the warmer of three.
As far as bears go, it is true that they fatten themselves, both during berry season (primarily July and August) and when the salmon are spawning later in the summer. Having said that, I tend to see them all through the summer, and I've never felt they were necessarily more commonplace in the later months.
Unfortunately, if the cruise option is the way you will be visiting, it's tough to get away from the hordes. Juneau has a resident population of about 30,000 people but well over a million tourists visit there every year. Think about that ratio packed into a tiny town and you'll get an appreciation of the situation.
When the wife and I go back there on vacation, we inevitably get a floatplane (or kayak) to stay at a Forest Service cabin for some unforgettable fun and solitude.
Basically, any way you can get away from the lead-you-by-the-nose tours is the way to go, in my opinion.