Mike, I'm not sure how much of a role oil plays in coloration of the crust. From what I understand, members usually mix in about 1-2% sugar to help with crust coloration while using oil for it's tenderizing effects on the crumb and questionable flavor profile.
If you are interested in a 3-4min bake, you can still use a modified broiler method. Just move the stone further away from the top broiler so that it is more like 8-10" away to extend the bake time. You'll have to do some testing to see what works best for you.