I've never fished in the Kenai. Not sure if the "combat fishing" stories are true or not. Not sure what kind of Alaskan experience you are looking for.
I live on Prince of Wales, and we have a fair amount of people show up to take advantage of the river fishing for silvers/pinks/dogs. I've had buddies come up and fish in Sept and literally wear their arms out in the rivers, and fish a different river every day. No king runs in our rivers though. The ocean fishing it top notch for kings, silvers, and halibut. If you are going to charter though, go to South Central, as our halibut limits are stupid low now. But a self guided package in SE would still be fun. I know some operations of of coffman cove will rent you a boat/truck and give you a place to stay. 10 days of that would probably be the same price as 3 days at a guided lodge. Hell, you can even do a few days of alpine deer hunting at the end of Aug too.