Either the "aftermarket ECM" actually is NOT designed for those mods or there's a real problem.
It should run very well if it has the correct ECM and that won't change, so make sure you FIX IT before you go messing with the tuning or ECM at all.
Assuming it's a tuning issue could lead to hair pulling, money, down time, many repetitive threads on here, and frustration for everyone. Even if you manage to tune the stumble away, you're just masking the real issue.
Once you figure out how to use whatever tuning software you choose, I would first check the EGO correction factor and AFV. 2 big clues to what's going on before you dump the box of tuning Legos on the carpet. High correction factors will show leaking intake seals, lazy O2 sensor, etc.