Natural dough preservatives

Naturally leavened all the way!

It's a method of scorching 5% of the recipe flour (with water equal to 5x the 5% flour wt) by heating the flour and water mixture to 149-F (65C). The flour gelatinizes. This is cooled and mixed into the recipe with the other recipe liquids and the recipe then proceeds normally. The gelatinized flour causes the loaf to retain more moisture after baking and the loaf is also more tender, lighter and fluffy. One result of retaining more moisture is a longer shelf life. This is for yeast breads. Haven't tried it on quick breads.

is used as a dough conditioner, iirc it (or rather, one of its oxidation products) will promote oven spring and volume + strengthen the gluten.  But I seriously doubt it improves bread keeping, perhaps rather the contrary.  

Personally I feel that as was posted above, using a natural leaven or sourdough, high hydration, long proofing times...are the ways to improve shelf life.  But of course, if you're selling your product you don't need to do what's best but what the customer buys.  

would be ginger which is a little food for the yeast (think of it as a snack) and it also acts as a mold inhibitor. Add about 1/4 tsp per loaf- you won't taste it. There's also potato flakes/flour (not starch!) which helps keep the bread moist/soft for longer. I have heard that adding more fats helps prevent staling. 

Crumb softeners like water roux prolong softness (by means of increasing water retention), but for the same reason they don't act like anti-mold, on the contrary. More water takes with it more risk to develop mold, it couldn't be otherwise.

Acids and spices are mold inhibitors, but also yeasts inhibitors, so if you add any of them you will also have to increase the amount of yeast/starter.