Last summer I grew cucamelon (Mexican sour gherkin, mouse melon, Melothria scabra) up an old bird cage usually used to support peas (and previously to house a pair of noisy doves).
I wired the cage through drainage holes of three pots and put two plants in each pot. When the vines reached the top of the cage, I attached a couple of wire shelves stood on end, making the full height nearly 2m. I could have cut the tips and let the vines grow around the cage — it was hardly covered.
Next year, four pots, three plants per pot, and plants started a little earlier. Maybe a few in the sunniest parts of the garden to scramble over the (crudely homemade) willow hurdle.
Melothria scabra is said to be perennial, and growers in colder climates are advised to lift the carrot and store it over winter. The roots I lifted were very small, and as the plants are easy to start from seed, I didn’t see any point in trying to keep them alive for six months in the basement. In a warmer zone (6 or 7), it might be possible.