For 50 miles of road and 10 miles of gravel I would probably stick with a road tire but go wide, something like the Challenge Strada Bianchi or the Gravelking slicks that
mstateglfr mentioned. Won't be too hard to improve on the gatorskins, which don't have especially good traction on pavement, let alone dirt. My experience with the Challenge tires is that they have not slowed me down on asphalt.
If you look at most gravel tires they have a pretty minimal tread. The slipping and sliding on gravel roads comes from the nature of gravel and dust itself, not the tire, and knobs aren't going to change the fact that gravel moves around underneath you. That said, this does not mean that knobs are completely decorative because if they were, then your gatorskins would be fine, and I definitely don't slide around as much with a gravel tires as I do with a smooth tire.
I've found that tires with a file tread like the Specialized Trigger Pro (rest in peace) roll surprisingly quickly on the road. However, there is a noticeable difference between them and a dedicated road tire, and the few times I've joined a road ride with my gravel tires I definitely had to work a lot harder to keep up.
But like other people have pointed out, those fire roads it sounds like you're on are going to be a challenge no matter what.