Recommendations on baking sopes?

The standard method of making sopes (and also huaraches, chalupas*, and gorditas*) can be summed up as:

1. form medium-thick masa patties
2. griddle those on both sides on a dry griddle
3. form the raised edges of the sopes
4. let sopes cool
5. shallow-fry the sopes on both sides
6. add toppings and serve

Sample instructions, here.

The problem with the shallow-frying is that it’s a very messy step, and sometimes you dip them in tomato sauce, making the frying even messier.

I’m wondering if step (5) could be replaced by baking them in a very hot oven, and if so what the optimal combination of time, temperature, and oil would be. I’ve found a few internet sources with oven-baked sopes, but none of them appear to be very well-tested. Has anyone actually tried this, or something similar, and if so what was your experience?

(* the traditional Mexican dishes by this name, not the Taco Bell versions, which are quite different)