No need to get an exhaust with a piggyback ecu + quickshifter combo. From my understanding, an aftermarket exhaust is mostly for weight saving, aesthetics, and sound.
Have you tried clutchless upshifting? If not, roll off the throttle at the same time as upshifting with no clutch. It should slip into gear. Googling "clutchless shifting" will give you a better explanation.
This is basically what a quickshifter does for you, it cuts the ignition for something like 50 - 100ms, which relieves pressure on the transmission allowing it to slip into the next gear.