One of my favourite ways to dress salad is to add some dried spices (garlic powder, oregano, black pepper, sea salt) and a little bit of olive oil. Good luck! Ranch dressing was my crack and I know it was a tough adjustment to enjoy my salads without it, but it can be done! :)
Soak cashews in water and drain, and then blend them to puree and add any of the following for taste and consistency.... water, lemon or lime juice (since you said no vinegar), roasted red pepper, parsley, onion, any veggie or spice.
Tahini blended with scallions, thyme.... maybe a mild rice vinegar if you can, oil.... kind of like a light, pour-able hummus.
Mash or puree avacado with flavorings.
Use a walnut-parsley-pesto (also great on grains and pasta).
I also whip soy milk until thick, drizzle safflower or canola oil, until its like mayo, then stir in a drop of lemon, salt, paprika, dried mustard.... whatever you like to make a creamy dressing. I use this whenever I make pasta salad. (the shortcut would be to use Veganaise as the base here).
Lastly, you could always put some olive oil in a jar with your favorite herbs and spices and let the flavors incorporate into the oil and drizzle that.... even sprinkle vegan parmesan.
Stop me now!!!! I know you have lots of restrictions, but maybe you'll find a good base here and adjust the flavorings to your needs. Its all pretty versatile.