OP: the symptoms you're describing are identical to the problems seen with a bad O2 sensor, especially the stuttering and SUDDEN acceleration. It's worth trying to replace or clean.
Of course, that's not the ONLY thing that might be wrong, but it is exactly what happens with bad O2 sensors. Very common, usually an easy fix. If you know a good shop, you can always buy the part, test, and return if that's not the problem. Move onto the next thing.