I used to believe that mirlitons could be grown in full sun. Not anymore. Intensive heat waves in the last few summers destroyed most vines that had been grown in full sun. The only ones that survived were in natural shade or had shade cloths. We learned the hard way that mirlitons need partial shade when there is prolonged heat above 95 degrees. That, along with substantial ground irrigation, can get us through another Heat Dome or intensive heat wave.
Build your trellis so you can easily mount a shade cloth over the vine. You won’t need it unless the temperatures stay above 95°. It can be thrown over the vine or mounted over it. Shade cloths come in different shading percentages, and we recommend 40% cloth with grommets so it does not blow away. They are available at Amazon and most big box stores. Shop around online to find one that will last for years. An Amazon link is here.