This is the business part of my lathe's tailstock:

The problem is, between the brass nut & the steel screw, there's around 0.1" play. As a result, particularly when drilling something "grabby", the drill has a tendancy to lunge forwards into the work, until the screw catches up. Not to mention the fact there's bugger all actual metal left in the nut's thread...
Making a replacement should be fairly easy, with the exception of internally threading the brass nut... I could, at a push, probably grind up an external threading tool, but I've no chance doing an internal one. I'd like to make both the shaft & nut new, so there's absolutely minimal play. Plus, it'll be good practice making a left-hand screw thread.
Therefore.... does anyone happen to have a 3/4" 5-tpi left-hand Acme tap I could borrow? I know RDG tools do one for 25 quid, but that seems to be a tad wasteful when I only expect to use the thing once...
Also, should I cut the nut in brass, or phosphor bronze? Based on the fact the one I've got is likely to be original, and between 70 & 80 years old, is there any point making it in anything harder than brass?