Two comments on this. The first is that I highly recommend an itinerary that includes Glacier Bay. The National Park Service limits the number of ships per day/per season that obtain a permit to enter Glacier Bay. It is a very worth while day on an Alaska cruise. As others have commented, on a one-way cruise to or from Alaska you see a lot more than RT Seattle and RT Seattle always includes Victoria BC so a non-Alaska port plus a sea day to consider vs the days actually in Alaska ports.
Second, pay very close attention to the itinerary port times and if you will be docked or tendered. You want as many hours in each port as possible, especially in August when the days start to get shorter. On our sailing, the Princess ships were docked at the pier and the NCL ships were anchored and tendering in several of our ports. Tendering adds a lot of time and frustration to your port day. Princess has Alaska “locked up”. They own the busses, rail cars, hotels etc. Other companies are outsourcing and in August the college labor has left for the season.
Just some things to consider.

I took the last cruise of the season which was first week of December. It was chilly, but beautiful. We even do the top of Denali. It was out of the clouds for 2 days. Beautiful and unusual.

What cruise line sailed in December?

We took that same cruise last year, last week of August-first week of Sept. Sun ship is ok but dated. Bring layers, weather can be fickle. Enjoy Alaska!

We've done two Alaska land/cruises with Princess. Not only are their lodges exceptional, they also have their own railcars to get you to some of the locations. You see so much more on the train than you ever will on a bus.

We usually do the land portion first. We like to see as much as we can while we are there. Whether it be rafting in Talkeetna or taking the tour up into Denali. There are endless options for things to see and do, whether it's through princess inhouse excursions or privately arranged.

Then after a week of going full speed, you get a nice relaxing cruise back to the mainland. Well, sort of relaxing. We still see as much as we can at each port stop.

No First part of Sept will probably be ok. Look up historical temp. Mornings a little cool and afternoons could be shorts and a tee shirt.

Late August should be fine, better chance to see the Northern Lights. Is it round trip or one way? If round trip to Seattle I think you won't see much, if any, of the inside passage. We went on Royal Caribbean from Vancouver BC to Seward, then booked a 5-day land tour through the cruise line ending up in Denali, then taking the glass dome train to Anchorage. If you can manage it, I would highly recommend doing so. It was the highlight of the trip.