Serious Eats: Talk

How do I keep cheese from oozing out of my enchiladas?

Back Story, when my Grandparents came to the U.S. from old Mexico back in the day, they settled in Dodge City Kansas. At the time my Abuelita had limited access to masa harina for corn tortillas, though she did have plenty of red chile, ristras as well as powdered.
Anyway, she was able to make flour tortillas and that is what she would make her rolled enchiladas with. Living in New Mexico people scoff when I wax about 'em , but trust me, they are DELICIOUS.
I want to make a big old batch for my Pops tomorrow, they are his favorites. They require some baking on low heat after being dipped in a pot of red chile then filled with cheese and onions.
The problem I have is opening the oven to find a bunch of rolled tortillas floating in a pool of molten cheese on a cookie sheet. Not a bad thing, just not the intended purpose. Is there something I can do to the cheese to help it stay set, so it will melt and not run? If this helps, I use a blend of sharp/mild Tillamook, and bake for about 20 mins. at about 250 degrees.
Thanks,
T

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