Distributism has been called a third way, in between capitalism and socialism; GK Chesterton put it best when he said "Capitalism suffers from too few capitalists, not too many".
The division of labor comes into play when you can trade your skills for other items you need in barter and friendship, or at worst, by using a local currency you obtained by owning your own means of production, while maintaining your ownership of basic production of food and shelter.
Once you exceed the bounds of *direct* barter and friendship, you run the risk of having imperfect information (of people lying to you in capitalism, or of people stealing from you in socialism).
Subsidiarity and Solidarity should be the goal, not mere profit.
"To me, the best economic system is essentially to take Adam Smith and mix in Pope Leo's adminitions (in so many words) to not screw each other. Is that consistent with distributism? And if not, why not?"
Add in 7 more papal documents by later popes about not screwing each other, and yes, that's completely consistent with distributism.
The only thing I'd add, comes *directly* from current economic situations in the global marketplace and in the United States- Big is Bad. Too big to fail is too big to succeed. As a rule, money is power, and absolute power corrupts absolutely; ANYBODY, even the most pious saint, will be corrupted by a love of money. And the more money you pile up under a single individual or corporation, the more power that individual or corporation has, the more corrupt that individual or corporation will become.
Far better to be a farmer, than to gain the whole world through your skills and lose your soul.