If you are deeply cutting, as in this case, the taper will not be in alignment with the bore. As I said before, it has to be removed, cleaned up by boring, and the last .002 to .005 taken with a reamer. The ONLY way to ensure concentricity and alignment.
Craig
what is the OD and length of your tailstock quill. Also what size of key way?
Craig, I agree with @Johnwa , your tool is probably rubbing. You could try to change the tool angle to give you more clearance. Also, raising it might work.
if you want, we can try to repair it using my SM1340. Your TS quill should fit nicely into the 4-jaw and we can first bore it as @Dabbler suggested (and you are trying) and then we can ream it with the reamer you have.