You are doing the right things.
You are using small threads, and if you are cutting threads on the lathe, by hand, such threads are fine pitch. As such they are incapable of dragging a Tailstock along the bed of a lathe..
The 0-80 ANF has a thread depth of only 0.008"
For fine pitch threads, you either need to use a Sliding Holder for Taps or Dies, to drive the Tap or Die Holder by hand when it is supported and aligned by a centre in the Tailsrtock. The Tailstock barrel will need to be advanced and retracted, at almost every turn, as the Tap or Die is moved forwards and backwards, as the thread is cut. Alternatively, a spring centre, such as a "Taptru" will do this
Using a Sliding Tailstock Die, or Tap holder has the advantage of keeping the thread square to the work so that it is not "drunken". (Also, fewer taps will be broken, since they do not take kindly to being bent! ).
It goes without saying that a lubricant, such as Trefolex, or Rocol RTD should be used, and that the ,tool should be withdrawn frequently to remove any swarf.
HTH
Howard