Pretty sure that closure is because of spawning timing.
Rodney has posted a lot of information and videos on bait fishing for the Kokanee - I'm sure you've check it out already. At this time of the year I think bait is the answer for any non-spawning kokanee.
I've been out a few times in the Fall many years ago and had the best success trolling with a small willow leaf gang troll with wedding ring spinner tipped with maggot. I also had some success with trolling green or brown sparkle leeches and Green Doc Spratleys but the catch rate was really low compared to the first two weeks when the lake opens in the Spring. Spring time I really only use a red micro leech with a gold or silver beadhead on an intermediate sink line.
I've stopped fishing Kawkawa in the Fall because the time or effort put in to catch a keepable fish was so poor compared to river fishing for salmon - so I opted for Salmon.
I'm not trying to discourage you from taking your Son to Kawkawa, it's always quality time spent whenever you can take your kid fishing so if you can find a nice day to get out - go for it and enjoy.