Dark Sun was a great setting. It is very much a product of the 90's, warts and all. It could stand to be updated, not watered down, but updated to be as groundbreaking as the original. Muls, like 1E half-orcs, need a rework. In a world of ecological apocalypse and magical tampering of evolution, why would Muls necessarily be 'bred' for slavery? Muls are just another way, like psionic ability, the natural world is making stronger candidates for survival.
Chattel Slavery doesn't need to be ever present. The Sorcerer Kings are in complete control. The templars, merchants, and nobles owe their position to them. The rest of the population is similar servitude without the need for echoes of history. Food, water, and safety are all limited resources. Control is easy for those with power. Slavery takes many forms after all.
I'd do a complete reboot. Not just a calendar advance. Set 5E Dark Sun after the appearance of the first Avangion. The Veiled Alliance becomes a crusade of preservers, a scourge to Freed City-States and those under the yoke of Sorcerer Kings. The Dragon still exists. How will the party navigate this chaotic land?
1. Dark Sun still is a great setting, and i see ways to make it work with 5e but you need to put on grognard googles xtreme for it to reach that tone. And since todays generation will not even remotely understand what that tone is - it is also useless to try and explain it to them, they do not know that rock'n'roll feeling because they never experienced all the circumstances themselves, it is like my parents telling me about ww2, they experienced it as kids but i will only get an idea on how it possibly was, but that's about it -
and since wotc wants to sell to younger people also, they will not do it right, basta, no use discussing it.
2. Muls are a crossbread between human and dwarves, a thing normally not possible in other settings, and muls are sterile like the namegiving horse/donkey crossbreed, so even if possible, there is no point in it.
With halfgiants it is even stated that their origins are because of magical help, since it would not work out the normal way.
But every race is stronger in DS so evolution parallel to the breeding of special slave races already did what you propagated. It is just muls not only are stronger, they also need less water than other races so in many circumstances they are more optimized. Being a bit dull they also do not tend to rebell as easy, as long as the basic needs are covered.
3. You do not navigate in DS. Travel is an adventure on its own, it is not taking the five o clock caravan from Tyr to Urik at fridays.