Actually John the lathe is good for alignment as you can see in the last picture. Both live centers in head & tail stocks line up perfect.
Pardon me. The tailstock point in the last picture looks lower than the headstock point. But not much. That much usually doesn't make much difference except for certain things. During a break in a demo I had to adjust our club lathe before Mark StLeger could complete the next critical step.
I didn't read all the posts here but if there is a misalignment problem in the threading jig due to welding, assembly, or part tolerances any machine shop (or hobbyist with the right tools could make it perfect if you wanted.
A mental sketch suggests that even threads cut at with the slightly tilted cutter angle should still work although the threads wouldn't be perfectly symmetrical. For a severe tilt the threads might need to be sloppy. Probably not a show-stopper for the relatively loose, short threading typical on wooden boxes and such. Could verify this with a thread gauge. Threads cut with my Baxter have been well-formed.
Lots of rain here today. Puts halt to my building site prep but doesn't stop me from processing more turning blanks in the shop. I have WAY too much wood. (sigh)
Yikes it must be cold where you live! I made a couple of tech transfer trips to Saskatoon, one in the dead of winter. I thought I was going to die just walking to my host's car. (He stopped at a mall so I could buy some gloves. "What!! You didn't bring gloves???) I did spend a couple of hours in customs on the first trip explaining that, yes, our trip was related to work, but no, we were not coming to take work away from Canadians but sharing ideas and brainstorming variations from our inventions that could bring jobs into Canada!
Even got to make a side trip on the way home to Banff and see the amazing ice sculptures at LakeLouise - something new to me.
JKJ