How to add richness to a vegan dough?
Olive oil! Or really, any oil you prefer. Vegan butters would probably work too, but I prefer a good quality olive oil. You can get ones that are pressed with other vegetables/herbs/fruit etc. for example olives pressed with lemon rinds makes for a stunning lemon olive oil.
Just sub out some oil for water/liquid. 
Or try adding spices, seeds, something to give it more elements of flavour, perhaps a dash of nutritional yeast would trick the taste buds.
Vegan baking is so chemically different from baking with dairy products that it really isn't always possible to create the same product.