My training is in historical approaches to ironwork, so that colors my steel advise. O1, O2, W1 or W2 would all make a useful tap or die. I like W1 for a number of reasons.
First, it is similar to a quality late 18th c. steel---- not identical but similar. If something like this was used historically, I ought to be able to use it too.
Second, it forges easily by hand and is very forgiving as long as it is not over heated. It responds to various oil quenches, a brine quench or just a plain, old, slacktub water quench depending on the results needed. I have made everything from forging hammers to drawknives to simple springs from it.
Third, it forge welds like a dream. This is critical when duplicating period style woodworking tools with high carbon steel laminated to wrought iron bodies.
Fourth, it is readily available in various sizes in most any industrial supply house as "water hardening drill rod". Pretty inexpensive, too.
I don't belong to the O1 fanclub. It hates water which I use a lot around the fire and it is further away from a simple 18th c. material. I also use quite a bit of recycled file material which I've been told is 1095. Again, a simple carbon steel. In fact, I've seen gunsmith- made screwplates that were clearly fashioned from old files.
Dan rightly warns of warping and decarburization.. Quench gently. Sometimes warpage can be removed at the tempering temperature. You can minimize decarb' by using a carbon rich fuel, heating in a reducing part of the fire, heating quickly and not overheating. As Dan suggests, casehardened mild steel would probably work. I'm pretty convinced that the period screwplates I've seen were either all steel or the working surfaces were. One I saw had plugs of steel welded into a wrought iron body for each opening in the plate.
If you are looking for British threading tools, try Tracy Tools in the UK. They seem to have everything and more. Do an internet search.
Just brainstorming: you can turn a bolt into a low grade tap by filing/grinding the end to a three or four sided taper. After casehardening with Kasenit, the corners of the taper act like rudimentary scrapers/cutters.
You've got a lot on your plate. PM if I can help further.
Good luck!