You have ovens, don't you have burners?An electric fry pan maybe?
My first question would be how many do you need to prepare all at once?
My recipe for chili rellenos is as follows:
Fire Roast Poblano chilis until black (or anaheim, but poblanos are better). You can use a small outdoor charcoal bbq for this. Wrap in plastic or zip locks for about 10 minutes then rinse gently under cold water removing most of the charred skin, cut carefully around the stem and remove the stem and seeds without cutting through the little pocket you've made. Rinse inside and leave to drain and dry on paper towels.
Stuff with stringy cheese of choice. Mexican queso preferable but munster and/or jack works. OR you could use a meat mix. There are a wide variety of recipes for mixtures, pork, walnuts, pomegranite...
After stuffed and dry, dust each with flour. They can now be refrigerated or frozen.
When preparing: Whip egg whites to soft peaks. Whip yolks and fold into whites.
Heat about 2" of oil (I love peanut oil for the flavor) to about med high in a frypan. Re-dust with flour and dip chilis in egg to coat and fry gently on each side until golden brown. Drain on paper towels. You can put them in a warming oven on parchment at this point. Do not wrap. I wouldn't store long after frying, unless you can refresh them in hot oil. You definitely don't want to deep fry rellenos and they fry pretty quickly so if you have a large saute pan or fry pan (or several) you can do a lot at once.
Serve with a fresh tomato sauce. A simple pureed tomato with a fresh serrano and a little salt. About a pound of tomatos to one chili. I'd coat the bottom of a serving pan with heated sauce (an inch or two) and float the rellenos on top. Dust with a little crumbled Cotija (like a Mexican feta) Garnish with sprigs of fresh cilantro.
I'm sure someone somewhere out there has a recipe for baked rellenos but I wouldn't personally recommend preparing them that way.
Another method that I haven't tried but might work would be to put about an inch of oil in a full pan and heat to 450 + degrees. (heat source on the bottom and place pan on bottom rack. Then - all at once - dip and place as many chilis in the pan as you can without touching and bake in the hot oil. For a full pan I'm guessing you could fit quite a few. (25 - 30+?) Very prep intensive but like I said, I'm guessing but it would seem that 450 degree oil is 450 degree oil no matter how you get it there. You'd just have to use a thermometer to make sure the oil gets hot and not put the rellenos in until it gets there. I'm using 450 because once you open the oven it's going to lose temp for a bit. You might want to use an even higher starting heat like 500? The rest is up to you as to how long to "oven fry" and checking progress before you flip them. I'm guessing at least 10 minutes until you need to check the first side for color? (just lift an edge of one). An oven with a decent window would work really well.
I thought about the pam method but I don't think it would work.
Then drain like you'd deep fried them.
Best recommendation is to play with the various recipes until you find something that works.
If I happen on a baked relleno recipe I'll throw it your direction.