In my area, some gourds are marginal simply because I don't have enough warm growing days. Here, they need FULL SUN and lots of room. I have to plant them in the ground. Even then, I often finally
get female blossoms just before first frost in mid-October... But I keep trying....
Is this bottle gourd or birdhouse gourd? I have had better success with the smaller birdhouse gourds that are about 8" tall and 5-6" across -- they mature faster and start producing female blossoms earlier. Gourds are prolific once they start to bear.
I think 4 hours is not enough sun. Definitely take down the umbrella and come up with another solution for the wilting problem. Some wilting during hot 90° day is normal for most cucurbits, but if yours are in containers that are too small, then you need to supply them with more even moisture and nutrients -- maybe some kind of self watering mechanism -- even as simple as water-filled recycled bottles and jugs with tiny holes in the bottom, or get those soda bottle watering spikes.
If you can, I would set the current containers on top of larger containers or tubs filled with rich potting mix and let them grow roots out of the current containers into the fresh supplemental supply. But if they are already clinging on trellis or something, I guess thats not an option. You could try burying trailing vines in containers of fresh potting mix as a supplemental source to grow roots into as well -- vines are flexible that way