Quiche- what am I doing wrong?

I got a copy of The Good Egg for Hanukkah. It’s a cookbook with egg recipes. It has many quiche recipes, and has instructions for making any quiche crustless. I like making the crustless quiches, because:

It’s healthier
It’s easier (the Dough Roller Gods don’t like me)
It takes less time and requires less equipment

There’s just one problem: the crustless quiches I make turn out runnier than quiche I’ve had frozen, in restaurants, etc.

The general recipe calls for 3 eggs (we use one real egg and 1 Egg Beaters, which is supposedly equivalent to 2 eggs), 1 cup of milk (we use skim), 1 cup of grated cheese, and 1-2 cups of whatever filling you want. You bake it at 350 for 25-30 minutes.

Anyone got any idea why these quiches are turning out runny? I have some theories:

  1. We’re not getting all the moisture out of the filling (fillings this has happened with have included frozen spinach (thawed, of course) and sauteed mushrooms)

  2. Using Egg Beaters instead of two of the eggs is making it take longer to set. But I use Egg Beaters in all sorts of baked things, and have never noticed this before.

  3. We should be cooking it at a higher temperature (the cookbook recommends 350 for crustless quiche, 375 for quiche with crust)

  4. Our oven is wonky (but this doesn’t seem to happen to anything else we bake). Getting a different stove or oven isn’t an option, because we rent.

  5. Crustless quiche just is this way.