Update . I got the latch out. I inadvertently ended up using the
Roger Shoaf method (thanks, RS) since every time I tried to finesse
the latch out, another part of the latch self-destructed. Yes, the
spring eventually appeared, and I removed it, and yes, I was able to
pull the latch out with a needle nosed pliers.

Also, I removed the the hinge pins, and no, the door would not come
off the hinges.



But yes, I got the latch out ! Yay. Thanks for the help.