I'm assuming you bought the tomos brand new. If it is a new tomos, its actually called the sprint. The bullits were the older models with a different engine. I would recommend calling it a sprint so people know what kind of parts you need and dont give you something that doesnt work.
And dont worry about the exhaust, as far as i know you have the standard a35 pipe on yours. The streetmate is like the luxry tomos moped. You bike shouldnt have a cat-converter nor have these problems. The only thing about your pipe is it is very restritive. Thats like the slowest pipe tomos ever made, but it works fine.