Back in the day I used to do loads of multiday touring- most weekends in fact. There were 3 or 4 of us and we all used Specialized Crossroads II. They were superb tyres. Narrow at 1.75 and with a low tread pattern. They would get sketchy on mud and wet grass but as most of the routes tended to be forest track, disused railway or country lane they were ideal.
In fact, IIRC, we did the original Coast to Coast (the Alfred Wainright version) on those tyres and that route took in every surface imaginable.
When distance is involved you need something fast rolling to conserve energy. Ultimate grip is useless as you are going to be heavily laden and only travelling at 4/10th speed anyhow.
Puncture resistance should be your main priority. Nothing worse than a few punctures to slow a group down. And remember- a heavily laden bike is more prone.