Chilli - yes
Cucumber - possibly in dappled shade but I start cucs in Mar/April as we go into winter
Eggplant - yes
Okra - yes
Pumpkin - see cucumber
Radish - In dappled shade or with shade cloth possibly
Rockmelon - Not easy with our humidity
Squash - see cucumber
Corn - yes
Sweet potato - yes
Tomato - possibly if you position them to avoid afternoon sun
Watermelon - the best time to plant in my opinion is Sept for harvest in Dec otherwise the humidity in summer is too much
Zucchini - see cucumber
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Perpetual spinach - will suffer a subtropical heat to an ok standard
Kang kong
Egyptian spinach
Rosella
Gourds
Basil
Verbena
Ginger
Turmeric
Galangal - might grow this out of the patch it can get pretty big
Cardamom leaf
Lettuce - in the dappled shade loose-leaf types will grow ok-ish with lots of water
Carrots - will also grow in dappled shade or protected by shade cloth
Walking onion
Garlic chives
Taro
Jerusalem artichoke
Snake bean
Brazilian spinach
Madagascar bean (lima)
That's about all I can think of at the moment.
you have no idea how helpful this list is. going to be seeking out many of these and giving them a go. thanks from a noobie gardener