Thanks everyone for your insights, both here and on my other thread about stuffing size
https://c34.org/bbs/index.php/topic,10826.0.html.
Yesterday I took my old (bent) bronze shaft and stuffing box that were replaced in 2019 into my living room and practiced pulling the stuffing out of the nut (and putting it back in). This was practice for later doing it on the boat, which is a couple hours away. The old nut had 2 rings of what look like 1/4" GTU.
I returned to the boat today to try out my new skills, and pulled one layer of stuffing out of the nut which revealed a lot more threads in the nut. The old stuffing that I pulled out, which was the "pre-stuffed" PTFE material in Catalina Direct's stuffing box linked above, looks like it's probably "WESTERN PACIFIC TRADING Flax Packing w/Teflon -1/4''
https://www.amazon.com/dp/B00DH3K2MS (Pet peeve: Catalina Direct is always annoyingly vague about the manufacturers of each of their items. You often don't know what you're buying until you get the delivery and see the brand name. I think that is borderline unethical behavior.) The flax was very hard to get out of the nut, and I noted that it had "squeezed" into the threads, and after getting it out I could clearly see where the threads had "cut into" the flax. (This had not happened yesterday when I pulled the 1/4" GTU out of my old nut.) The Teflon flax appeared to be 1/4" square, and I later confirmed that there were three rings. Since this was flax, I suspect that it had sucked up some lubricant that I had put onto the shaft and swelled enough for the three rings to prevent the threads from grabbing. I'm really glad the boat was not in the water when this happened.
Unfortunately, even with more threads available I still could not get the nut back on to the stuffing box. So I decided the stuffing box had to come off. There was definitely not enough room in front of the coupler to fit any sort of coupler puller, so I decided I had no option but to tape a stack of coins to the end of the shaft and bolt the coupler onto the transmission flange to push the shaft off the coupler. I had heard the horror stories of the danger of cracking the transmission flange when doing this, but it was really quite easy. Very little tightening of the bolts was needed, and I was able to do much of it by hand without even a wrench. I did have to unbolt the coupler several times and add more coins to the stack, but with time, patience, lots of PB Blaster, and a gentle touch, the coupler was off.
Once I brought the stuffing box home I was able to get the nut to engage, but it is really super-tight (could not do it by hand) and I can see visible galling of the threads on both the nut and stuffing box. The stuffing box is toast - I can re-use the lock nut, but that's it. I would just buy a new one, but space constraints would require me to get another one from Catalina Direct, since in 2019 I verified that the Buck Algonquin ones (and ones from other suppliers) are all larger and probably wouldn't fit behind the transmission. CD's boxes only come pre-stuffed, and I don't want to use their PTFE-flax due to the swelling issue (I realize I could just take it out and replace it). First I think I'm going to try cleaning up the old stuffing box that was replaced in 2019 and re-use that. It was replaced because it was part of the surveyor's insurance claim, but there is absolutely no damage to it except for the lock nut that the yard staff mangled pretty badly badly getting it off, but the lock nut from the "new" stuffing box can be used instead. So between the two stuffing boxes, I can cobble together one with some new packing material.
I've been reading a lot about packing materials, and might go with two wraps of 1/4" Gore GFO since Maine Sail says it cuts cleaner than the GTU. Rod gives ominous warnings about all the graphite materials being banned by ABYC, but no clear direction on what to use instead since his own Teflon material has not gone commercial.
https://marinehowto.com/re-packing-a-traditional-stuffing-box/ FWIW, I'm really intrigued by this material made from woven PTFE filament, but I cannot bring myself to use something that has not been fully tested for marine use. Part of me wonders whether this is the stuff that Rod was testing on his boat:
https://www.amazon.com/dp/B07HGP5VWR