Mystery Veg Identified: Balsam Pear
The mystery fruit has been identified!
Daniel Jalkut suggested that it looked like this photo claiming to be a Balsam Apple. I think the photo is mislabeled and this is actually a Balsam Pear or Bitter Gourd.
This difference appears to be important as the Balsam Apple is toxic while the Balsam Pear / Bitter Gourd can be cooked and eaten. I hope I find another gourd on the vine as I’m looking forward to tasting it.