Many thanks to Max Gruner for thinking this up and posting it. I've hiked up here a bunch with my kids, but never would have tried to hook all the trails together otherwise. It's a really nice area with some good variety and lots of runnable terrain (plus the green and aqua trails have these sections with ferns that are just so beautiful!). I scouted the route a couple of weeks ago, and then did it for real today. In keeping with ecology and high gas prices, I biked 11 miles to the parking lot and then home after I was done (the rides are not included in my file or activity record). I started and stopped my run exactly at the information kiosk in the lower lot.
There are many ways to run all the trails up here, and you can see on the Garmin link how I did it. The route I picked had a nice flow and made sense to me. There's no way to do it without overlapping some sections (I overlapped the same as Max did and think there's no way to do it that's more efficient). A quick note: the orange/green connector has a trail segment (marked for bikes but ok on foot) that is officially blazed but is not on the official trail map. I ran that as well as the foot trail, figuring it's in the spirit of running all the trails, but I think it's ok if somebody excludes it. I think it adds some distance but is less technical, so probably a wash in overall time. There's also an unblazed herd trail connecting orange with blue, which would knock off some distance, but I didn't take that for obvious reasons.
I ran solo, unsupported, which was easily achievable on a route of this length. I only saw one person the whole time, launching a kayak. Week days, these trails are very quiet.
A beautiful experience and I encourage anybody local to go check it out.