How to make a restaurant style meatless Hot and Sour Soup
For heat, I recommend chili oil as opposed to a paste. That and white pepper should give you a pretty solid heat component. Even though the thought initially made me go EEEEEEW, ATK does recommend a a 50/50 combination of Balsamic and red wine vinegars as a replacement for the ideal Black Chinese Vinegar, which is probably what great Chinese restaurants use. Do you eat eggs? If so, I'd certainly use one. Here's the technique, again from ATK " Without stirring soup, use soupspoon to slowly drizzle very thin streams of egg mixture (1/2 tsp corntarch, 1 tsp water beaten with 1 egg) into pot in circular motion. Let soup sit 1 minute, then return saucepan to medium-high heat. Bring soup to gentle boil, then immediately remove from heat. Gently stir soup once to evenly distribute egg."

You probably should considerably up your soy sauce. Consider too your mushrooms. "Assorted" can mean just about anything. Some mushrooms are very strongly flavored in a way that just plain clashes with Chinese Hot and Sour. That could very well account for the barnyard odor you describe. I'd recommend sticking to shiitake/oyster/woodear if you can.