With 150 days to harvest, Chayote (Sicyos edulis; it has several local names) seems like a stretch, but possible contender.
This is a viviparous (seed starts germinating inside the fruit), perennial vine, up to 8 years but best up to 3 years. Grows quickly. Produces increasingly as with each year. DELICIOUS. I eat as much of as possible whenever I’m in the Caribbean and Mexico and Mesoamerica. Fruit is tasty eaten raw and cooked. Apparently leaves, stems and roots are all edible too.
Need to figure out how to preserve it and how to overwinter the vine or a new plant. My best guess is that in warmer climates, fruits drop and new vines start (although some seeds germinate while still on the vine). So it almost meets Paul’s criteria.
I’m itching to try it here in zone 7b. Probably best for folks in the south; ideal in tropics (and Florida?). It can be started indoors, and summers here are stretching into autumns more and more. Maybe with a passive, solar greenhouse this would be a good option.
Germinating and growing experiment in Taos,
NM and general information described here:
https://www.motherearthgardener.com/plant-profiles/chayote-on-the-rise-zm0z20szbut/
Looks like folks in BC are experimenting with varieties that are more cold adapted (article comments are helpful):
https://bcfarmsandfood.com/chayote-squash-new-staple-crop-northern-gardens
This gardener in the Virginia piedmont grows it for its shoots:
https://www.laughingduckgardens.com/2009/01/29/growing-chayote-in-virginia/
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