I'm making Kolaches (a Czech semi-sweetened dough with a sweet filling), but I'm challenging myself to cook vegan, and therefore can't use an egg. I've got a bunch of recipes, but all of them are semi-enriched, i.e. have egg, milk, and added fat. I've got replacements for everything else, except the egg. 
What are things people have used for eggs in yeast breads. It shouldn't need to be a binder or leaven, just enrich. I've seen suggestions for sweet potato, just add oil, tofu. Anyone have any experience with enriching yeast doughs without eggs?