I don't think I would use slime tubes on GD, but using tubeless tires with some good sealant is a great idea. The slime tubes are pretty heavy and get pretty mediocre reviews. If you are going to use a sealant, use tubeless tires.
I've used tubeless tires on the Idaho Hot Springs route and on about 800 miles of the Great Divide. I was using 2.2 conti tubeless tires and orange seal endurance sealant. While the tires are "tubeless ready" the rims, which are several years old, were not. I used 1" gorilla tape to seal the rim. It worked great.
However, about 6 months ago I was coming down a gravel hill on a gravel bike with 40 mm tubeless tires (and tubeless rims) and had a stone cut the sidewall, which the sealant couldn't seal. I did have a sidewall patch and spare tube to get me home. After I got home I repaired the sidewall by sewing it up using a curved furniture sewing needle with 20 lb fishing line. I also put an auto tubeless repair patch on the inside, added some new sealant and the tire was good to go. It has worked fine for about 500 miles.
If you're using tubeless tires on the GD I suggest you carry a spare tube or two, along with the sewing needle/fishing line, an old piece of sidewall, a conventional patch kit and a pump. Fortunately, I never had a flat on either the Hot Springs or GD. While the sealant will seal off all of the small routine punctures, it will not seal a sidewall cut. I have not tried the tubeless tires repair kits, so I don't know how effective they are.
I think getting a tubeless tire to properly set the bead just using a hand pump after a flat would be very difficult. So the spare tube and sidewall repair kit is pretty important on the GD. If the tire goes flat, but you don't have to remove the tire and the bead is still good, you might have have some luck just adding more sealant and using a hand pump.
If you do decide to go tubeless, spend some time before your trip getting a feel for putting the tubeless tires on and removing the core to insert the sealant. The big benefit of tubeless is that you can run the pressure pretty low, helping you roll over some of rocks you will be encountering.
While the whole tubeless thing sounds a bit daunting at first, it really isn't that big of a deal once you you do it a couple of times. I think the benefits on a ride like the GD are substantial since it will really minimize your flats. But you gotta be prepared for the "shit happens" aspect of a ride on the GD.