So after experimenting a lot, I've decided to drop Mai for Billy.
Currently, my team is Billy/Ash/Kyo, but I feel like there's something missing. I think Billy's a lot more solid than Mai, especially for my play style. I can't figure out a solid and consistent anti air with her.
Other characters that I've been toying with lately, and I really like are: Yuri, Robert, and Shen. The only person I'm willing to part with in my team is Billy at this point. Ash and Kyo are definitely fitted to the way I play fighting games, which is a semi rushdown, semi zoning style. I can do some stuff with Kim, Terry, and Takuma as well, but I don't think I like them that much. Kim's fun for rushdown though.