Going to have two sets of wheels, one more tarmac/smooth oriented and 700c, and this set, the stock 650b wheels as long as they last for bigger days on dirt roads in and around Sun Valley, Idaho. Where it is usually kitty litter/ball bearings/loose over hard, punctuated by sometimes sharp rocks. The stock WTB Byway 47’s do not grip well enough climbing, and do not inspire confidence for me descending. My Kona Libre will take up to somewhere in the 50-52 mm, or 2.0-2.1 range, so figured for those dirt oriented days, may as well load up those 650b wheels with some tire that has some tread and grip. And I will be running tubeless.
Since I already have the Juniper Ridges, that I was considering selling, but now have looked at combos, I am now thinking the Maxxis Ikon 2.2. (EDIT, may not fit, will have to look for something kinda similar.) up front, and running one of the juniper Ridges in the rear, saving the other for later. I know I like that Maxxis feel up front from my mountain bike, and I know from other riders that they like the Ikon around here, so should work for up front, and the Rene Herse’s can do the rolling in the rear.
Nothing grips in the conditions you describe. Big knobs will slide over the top stuff and not dig into the bottom because, well, its hard. That describes the dry, desert-like conditions where I ride. A big tire as low as you can keep the pressure is about the best you can do. I've used the Byway and it did not grip any better or worse than the mtb tires I used in similar conditions. The Race and SpeedKings won't fit but I've used a Thunder Burt to good effect as I have the G-One Speed. I think they make the Speed and All-Round in 2.0 sizes, but I have not considered them since Schwalbe switched to Addix Speedgrip, which is a really slow compound, but if speed is not your worry then the All-Round might work for you. The one I used for a while was pretty versatile. Heck, if speed is not your concern then you can just ride the Maxxis, which are even slower than the Speedgrip Schwalbe tires and might grip better. If speed does matter, then I would try the Thunder Burt. Just a caution, it measures 54 on my 29 id rim, so it is going to be close to your max on a 21-25 ID rim.
The Umtanum Ridge are generally not a bad idea, both front and back as they're probably not much slower than the Byway anyway (esp if you trust RH roll-down tests). But I agree with @ccand51997 that nothing grips well in these conditions. The UR tires would offer the distinct advantage in soft/mud (or maybe snow), basically the rule I go by is that if you can't see the tire-tread tracks on the road, the tread probably isn't doing anything useful.
I do really like Schwalbe Thunder Burt. I have a set of G-One speed in 2.35" that I need to sell, but sounds like that would be too large for your frame.
Other than nasty clay mud, loose over hard is probably the worst condition we encounter. As has been stated already... nothing really works well. Every corner at speed is a crash waiting to happen. The only tire that I have used (and this was on an MTB) that worked "well" in these conditions was the old soft compound (they change the name every year, so I don't recall which one exactly) Schwalbe Rocket Ron. Fairly widely spaced knob with decent enough height to get through the kitty litter and that soft compound with siped knobs worked well once if got through to the "hard". They "look" slow, but were actually as fast as some of the dedicated XC tires but worked in a lot more varied conditions. I have no idea if they make something in a gravel size that will fit your bike (my wife's 27.5 x 2.2 RR's actually fit on my Warbird) but you might go down that road a bit and see what you find.
Agree with the Rocket Ron [27.5x2.1] comment, for dry riding. In our local pea gravel, the grip is good climbing. Does the job descending, though I'm a careful/cautious descender all the time.
Across mixed riding surfaces they roll good enough.
Have used the red stripe Addix ??? back and front. But in the old Schwalbe compounds only. Not a fan of the new/slower ones.
My first thought for the front [descending] was the Continental Cross King but those are 2.2. This comes in a Protection version which has a fairly stiff sidewall. My riding feel preference is the supple Racesport option, but those could be too fragile for your riding conditions.
Re the ThunderBurt comment, Kenda has the Sabre Pro which has a touch more knob height in the center, and taller side knobs. I think they come in a 2.0/2.05? One of those in the rear would have more climbing grip than your WTB. Rolling speed to me is about par with the liteskin ThunderBurt. The non-TR model would be best suited for you.