Unless you put a tight fitting piece of round stock in the end of the spindle I'm pretty sure it will be severely out of round and as
@phaxtris says it will be badly marred by the pipe wrench.
I see three choices but there has to be more:
1 - as Susq suggests, machine it off
2 - Split the BP with a dremel, that will relieve the pressure and allow you to spin it off. Being careful not to hit the threads.
3 - remove the spindle and put it in the freezer for a couple days to get a good soaking, then use the soft jaws to secure it in the vise and heat the BP with the propane torch. Use your jig (which should be still attached) and wrench to unscrew the BP.
Number three is what worked for me and the BP was fine to reuse but the whole process was a bit of a pita, I did however gain good understanding of the inner workings of the machine. My machine came from a school (of hard knocks) and had the gouges in the compound to prove it, I don't think it ad ever been off the spindle. It will come off, you just need to find the least destructive method to do it.
If you don't have the manual it can be downloaded from SM for free.
https://standardmodernlathes.com/resources.html
Good luck