I garden right next to a deer superhighway. I've successfully grown cosmos, marigolds, and zinnias. I haven't tried Mexican sunflower.

Do a search for deer resistant plants and you will find much info and hundreds of plant ideas. They haven't eaten any of your listed flowers in my yard, including Tithonia (Mexican sunflower). But fawns will try anything. Good luck.

deer resistant plants

Well, something just ate my cosmos up. It might be a woodchuck though, they eat everything.

Deer, as a general rule (not when they are hungry) don't like strong smells, poisonous plants (think milkweed) or plants with a course texture. So they generally stay away from regular sunflowers, but Mexican sunflowers are softer and deer love anything soft and lush. If you plant the least desirable plants on the outside of your garden it helps. Definitely don't lure them in. There's a long list of perennials, too: yarrow, tansy, swamp milkweed, common milkweed, hellebores, rudbeckia, coneflower. Might make a nice border that comes back every year that will deter deer.

I keep reading about deer-resistant, not deer-proof! After all, it's just a suggestion to them that they aren't welcome! ha