.... Nothing you can do because it locks when it wants and unlocks when it wants and isn't smooth. Drive/drove it then 30+K a year then.
I'm not saying you're wrong to not want a Detroit in the rear for your usage, but automatic lockers are completely predictable when you understand how they work. There are no "lock when it wants and unlocks when it wants" surprises.
That said, they often aren't smooth, and can be a handful on slippery surfaces, so they aren't for everyone (and you're certainly not alone in hating them). So please do not take this in any way to be saying that you (or anyone else) should give automatic lockers another try. Your experience and your conclusions are very valid.
Automatic lockers always unlock when one tire wants to go faster than the other. Period. They never stick or hang up. When you are going around a corner they will always freely allow the outside tire to go faster.
And they always lock when neither tire wants to go faster than the ring gear. Period. It doesn't take getting on the power to lock them. Power has nothing to do with how they work. It's all based on relative speed.
But yes, they can be objectionable. Why? Mostly because they unlock so easily. When you are going around a corner they unlock because the outside tire wants to go faster. So if you get on the power you are only driving the inside tire. That makes it very easy to spin that tire. When you do, it catches up to the outside tire, and now neither tire is trying to go faster so it locks again, and they are rather harsh, so it locks right NOW. That makes it easy to break the outside tire loose too, and now you have the back end coming around.
If you understand that and are willing to "drive to the vehicle" and avoid breaking the inside tire loose, it's really quite easy to tolerate an automatic locker in the rear in most circumstances.
But back to your experiences. Driving in snow it's often impossible to avoid spinning the inside tire, so it can become a handful. Towing a trailer makes it worse, because you need to put more power to the ground to move the additional weight, but you don't have much more weight on the tires helping your traction, so you are that much more likely to spin the inside tire.
And when you are on slippery sidehills nothing comes close to the stability of an open diff (or an unlocked selectable locker). A spinning tire doesn't care which way it goes, so the only way to maintain stability is to not spin at least one tire per axle. The strength of all diffs other than opens is that they make it possible to put power to both tires so both tires will spin. So yes, for slippery sidehills selectable lockers are really the only option.