Blend all crema ingredients in a food processor until smooth. Season with salt to taste before refrigerating until ready to serve.
Mix all salsa ingredients in a medium bowl and season with salt. Set aside at room temperature.
Prepare the grill for direct cooking over medium heat (350-450 degrees F).
Generously brush the mushroom caps, onion slices and pepper pieces with oil and season evenly with the Santa Fe seasoning.
Brush the cooking grates clean. Grill the mushrooms, onions, and peppers over direct medium heat, with the lid closed as much as possible, until browned and tender, turning occasionally. The mushrooms will take 12 to 15 minutes, the onion will take 8-10 minutes, and the bell pepper will take 6 to 8 minutes. If necessary, to prevent the mushrooms from drying out, occasionally brush them with a bit more oil. Remove the vegetables from the grill and scrape off any blackened areas of the peppers. Cut the vegetables into thin strips.
Grill the tortillas on one side over direct medium heat, with the lid open, just until warm, 10 to 20 seconds. Turn them over, top each one with ¼ cup of cheese and grill just until the cheese melts. Remove from the grill and assemble the tostados with the grilled vegetables, salsa and crema.