Thanks, Simon. I think a lot of what you see on the internet makes you think the process is very linear and one-and-done. Nice to capture the the more iterative and nuanced process of an expert! Thanks for the thorough walk through.
On the topic of cutting the nut...how has not not really been covered. Here's a web page that does a reasonable review of virtually every way I have heard of.
I think there is pretty much consensus that the best way to cut nuts is with high quality nut files. Most people here seem to have Hosco or StewMac. I have heard that the Uo-Chikyu files are great.
Unfortunately a good set of nut files will run you about the cost of a cheap kit. A great complete set for bass, acoustic, classical and electric could put you in Warmoth kit territory.
Being a cheapskate, I have not (yet) invested in decent set of good files. I'll let others chime about minimum needs for files...
For those considering the cheap approaches you'll see on the web, IMHO forget about using the torch cleaners on a guitar. Bass strings are thick enough that the "cleaner" diameter gives it some stiffness, even for the G string. But for guitar they are just too flimsy. I don't know how anyone can get a straight slot using them. I tried to modify a jewler's saw to do it. It was a waste of time.
I have done all my bass nuts with torch cleaners. However, the review in the link matches my experience. It takes a LONG time. Your hands will be very sore when you finish if you do it at a setting, and you will have gone through a very long playlist doing it. But it can be done.
On the guitar nuts I have done, I have cut teeth into a sacrificial feeler gauge set. It works reasonably well. I wouldn't do it with a triangle file. Get a rotary tool and cutting disk. They are cheap too and you can use them for a lot of things.
The feeler gauge approach is easier than the torch cleaner approach, but feeler gauges don't come big enough for bass strings.
While these approaches work, I can definitely say that every nut I cut makes me wish for good nut files. EVERYONE who has tried the cheap ones on this forum, to the best of my knowledge, says that the cheap ones are a complete waste of money and do a terrible job. I haven't bought any for that reason. But I really would like a good set of nut files...probably just a matter of time.