Not an complete answer but a clue-
I have noticed that some hot pockets will come with a cardboard cage that seems to be lined with very thin foil. In the microwave the hot pockets are actually browned. It would seem that the foil is able to heat up past 212F and do the job.
I have seen products that seem to do the same thing:
http://www.amazon.com/Corning-Microwave-Browning-Grill-Handles/dp/B003YQGMY0/
but I have not used them.
I haven't been brave enough to experiment because of the danger of fire etc. Good luck on your quest.
As eggs are a very versatile ingredient: when substituting, it is important to determine whether the eggs are being used as a leavening agent or binder (or both). In recipes where the egg is used primarily as a leavening agent, I have used a mixture of baking powder (not soda), water, and vegetable oil in a 2:3:3 ratio, though you may want to experiment with the proportions depending upon your recipe. You may also need to vary the amount of other liquid in the recipe.
Where the egg is used primarily as a binder, you could use banana, applesauce, or gelatin, depending upon the recipe (obviously, you'll probably want to avoid the fruits in a savory recipe). I've used, and been thoroughly disappointed with, the available commercial "egg replacers" and don't recommend them for any purpose. I've heard of using flax, but have no personal experience with it.
However: as the father of (and resident chef for) a young child with egg and milk allergy, it is my experience that successfully substituting for eggs is very difficult. For breads in particular, I don't even bother with recipes that call for eggs or milk, and favor those that use the basic 3 (4): flour, water, yeast (salt).
Best Answer
You could always try using vegetable, corn, or light/regular olive oil, vegan margarine, or light corn syrup thinned with a bit of water (to prevent over browning):
I also saw something here that mentioned the use of soy milk, but you said it didn't brown well. If it didn't brown at all, then it is most likely because you were using unsweetened soy milk (remember, sugar browns when exposed to heat).