Nick, THAT'S the idea! Time does fly when you are enjoying yourself.
The suggestion to make accessories for the lathe is a good one. You learn, and you end up with something that is useful. Have to admit that I do not machine my Morse Taper Arbors; I buy them from Arc EuroTrade. (They are near Leicester, so about an hour's drive from me, on the edge of Fenland, although their despatch of an order is usually same day).
There are other suppliers who can supply such things, but prices , and sometimes quality, can vary
(Had a bit of a discussion this morning persuading AET to DELAY despatch for a couple of days, so that I can be at home next week to receive. Otherwise I have a few miles to drive to collect from the sorting office).
A Tailstock Die Holder is a very good item to make, pretty straightforward turning. The only difficult thing about the tapping is the correct angular spacing for the grubscrews in each holder, the middle one is easy!.
If making, I would buy an arbor, (COWARD!) and then fit it into the Lathe Mandrel to bore it to take an extension (Look at various sites for a picture of what you should end up with). Having fitted the extension into the MT arbor (use the "heat and freeze" technique with a suitable interference – less than a thou, and with SHMBO permission to use the freezer) With the extended arbor back in the mandrel, the extension should be skimmed to just under the size of the bore in the basic Die Holder. This will allow a little "float" and reduce friction.
A stud screwed into a tapping on the side of the holder, rests against the toolpost to prevent rotation. Don't try holding it under power, in case anything jams. You can replace a broken die or tap, but broken fingers take a lot longer to repair, and no one stocks replacements. (Another thing that you could make is a Mandrel Handle to allow you to turn the Lathe Mandrel by hand for cutting threads with Taps and Dies. BUT DO NOT forget to remove it before you start the lathe under power).
Take a look at various sites, to see what a Tailstock Die Holder, and other useful things look like.
I made a Tap Holder to use on the same arbor. Found out the hard way that a 40tpi thread will not pull a big Tailstock along without stripping. At a pinch, a drill chuck on a sleeve will do the job, but uses more space than the ER 25 Collet holder that I made up..
You will be surprised just how tightly a tap has to be held. to prevent slipping. A useful safety factor that probably saves a lot of broken Taps. Once at that stage, you can always take the job out, hold it in a bench vice and complete tapping using a Tap Wrench.
I've rambled on for far too long. Fellow club members will tell you and show you similar gadgets.
Howard