"I would rather jump in headfirst and go for it."
I would just heed that impulse, Ken, if I were you. Hiking solo is a very different experience from group outings in that it will allow you to bring your own senses and judgment more into play, without the necessity to consider the needs, opinions, limitations, etc, of others. You already have the necessary skills and judgment; this is a golden opportunity to put them to use. Besides, you won't really be that alone on a Rae Lakes Loop. As for nothing to do for 4 hours in camp, hike around and explore the area. 60 Lakes Basin would be a nice 4 hour hike from a Rae Lakes area campsite. In general, if I have time after setting camp, I always hike around and explore as much of the surroundings as time, daylight, and energy allow and usually find the experience very rewarding. I hope you follow through with this.