You have to be careful with the stumble. Could be anything. Plug going bad, coil or AFM. Does the computer show any log of faults? Do you have access to a code reader?
Does it ALWAYS surge or miss at that particular rev range or when you slowly apply throttle?
Had a similar issue in my father in laws BH5 not so long ago. Replaced the coils and new plugs and issue solved apart from some cold idle issues which was sorted with new AFM. I noticed it logged an o2 sensor fault too so im replacing that this weekend.
Stumble or misses or surges that are minor are generally those 4 things. AFM, o2, coils or plugs. Does it fart around when its cold?
Your searching idle could be your TPS not set correctly also. Be the easiest and cheapest thing to check. Its free with a multimeter.