By "braces", are you meaning just strut bars (lower), or genuine chassis braces?
Chassis bracing puts you all the way up to DSP or maybe even SM, not sure where they draw the line. The Azenis are legal in any class, and the Toyos would be fine in G Stock(Ion Redline is not an ES car, but a GS car, like the Cooper S). If I were you, I'd just ask the GS guys if you can run with the braces, rather than trying to go to a prepared or modified class. I suspect they'll be fine with it unless you kick all their asses. :)
Seriously, if that's your only significant mod, just run Stock and clear it with your competition.
Edit: Just realized you were talking about your Mazda. Other than my inability to read, same advice.