I got stuck in King Salmon once due to an Alaska Air flight delay. Was very difficult to find lodging for one night at the last minute. Fortunately the staff at the Alaska Air lounge in Anchorage was very helpful in giving us some options. It was years ago so I don't recall where we stayed.
With 8 of you I would try for a flight with a different airline. I sed Branch River Aur once and they were much better than Katmai Air. Much less restrictive weight allowance too.
If you use Katmai Air - or any company for that matter - they run constant flights all day and would put you on ac flight to get you there or back. Even with Branch River I doubt they would hold all of you up if one didn't arrive until late.
Not much to do in King Salmon. I think there is inner place to eat out. Very small town.
You might look into the discount books - Toursaver and Northern Lights - to see if you can save on things like the Valley of 10,000 Smokes tour. Just that tour alone would pay for the book.
There is a Dumpling Mountain hike behind the campground that I have not done but I heard is interesting.
I would consider bringing some food. Are all meals included? I have only tent camped three times at Brooks. I brought most of my own food. That way I could stay at the viewing platform during meal times at the lodge - usually less crowded at those times. You can't have food in your cabins but there is a food locker near the NPS office and a place to eat inside an electric fence. Just a thought. Get to the platform early when it opens. Less crowded with fewer day trippers early and late in the day.
I would leave the 4 hour layover in King Salmon just in case.
Have a great time. When are you going? I hope July or September which are the peak times for Brooks.