I decided to put my advice where my mouth is and headed over to Dona Torta for my first order of perritos Mexicanos, still very much on offer at the torta superstore.
The Dona Torta version is three decent dogs, each split down the middle and wrapped in cheese, bacon, and a corn tortilla in that order. The whole thing is deep fried into a sort of red hot flauta/taco dorado, then placed on some lettuce, covered with lots of very hot, thin sauce (that used for the enchilada preps, including tortas ahogadas), and a generous squirt of yellow mustard. It all works beautifully for me. Four bucks an order. I was met with some skepticism from the staff, especially regarding my tolerance for the sauce, but they came through in the end.
I inquired whether one could order the dogs in bread rather than a tortilla. The problem seems to be that Dona Torta's only rolls are their humongous bolillos, used for the tortas. Maybe three or four dogs could be loaded into one of these rolls, but the traditional hot dog on a bun can't be accomplished at DT.
I also asked whether this particular style of dog could be found in a particular part of Mexico. Unfortunately, the better and more knowledgeable cook (wiry guy with mustache) was not on hand. I received a reply along the lines of "I don't know, I just work here." Anyway, I encourage everyone to try this healthy treat for something different.