Practically nothing you wrote made sense to me.
Sounds like you want an inserted ball mill 1.250 diameter 6.750 long minimum.
How about a Kennemetal KDMB1250R827A125SN? It is 8.25 overall, but the neck down is on 3.150. So you would have to turn it back at least 3.600 more for your clearance.
Product Detail - 2878433
They might have others available. I am not going to spend my time searching harder.