Whenever you fertilize, don't fertilize with nitrogen near the end of your harvest (it seems to be able to take taste out of the fruit). Using monopotassium phosphate near the end doesn't seem to hurt the flavor, however, and the phosphorus may even encourage faster ripening. It seems to me that nitrogen should primarily be used earlier on, if at all (before the fruit gets very big). Phosphorus and potassium can probably be used any time without significant repercussions to the plants (although maybe to the water supply), so long as you don't use too much. You might try forgoing the fertilizer (or using it very sparingly) and saving your seeds every year to replant the next. According to what I've read, they should become better-adapted to your climate and soil, and get used to having less fertilizer. That's not to say they won't need nutrients, but they in theory should be better at utilizing what is available. You might also consider creating landraces. If you move around a lot, though, this might not be the best option.

Melothia scarba aka Mexican sour gherkins. P

While I have never heard about this before, it sounds like a good plant to try. When in doubt, I always go with a bit more shade on a new plant.

I agree with Larry, particularly if you're in an area that is relatively dry in summer. Melons like lots of moisture (though not excessive moisture as they mature because it ruins their flavor) and if they are on top of a hill, too much of the moisture may run downhill before soaking deeply into the soil. It kinda depends on how high the hill is and also on how heavy the clay is. Most people here in my area grow their melons in the relatively flat bottom lands, particularly where there is sugar sand or sandy loam that allows their roots to grow freely. I grow melons in a narrow band of sandy soil at one end of my mostly clay garden. I've also grown them in highly-amended clay soil in raised beds, but in a rainy year, that soil can stay too wet for them and then the plants themselves will have disease issues. By the use of the term hill, if you mean a slight rise in the land, it likely will be okay and won't drain too fast, and will function like a raised bed. Still, without knowing if you are in an area that averages 40-50" of rain per year versus one that averages 10-20", we're only guessing. I even tailor my melon planting to the weather I anticipate we will have in a given year. If I am expecting summer rainfall to be scarce, I plant the melons at grade level in sandy soil amended with compost. In that looser sandy soil they can spread their roots endlessly in the search for more moisture. If I am expecting late spring and summer rainfall to be heavy, I plant in the highest raised bed I have, which is highly amended clay, so excess moisture can drain away from the plants. Sometimes you just have to experiment with planting different ways in order to figure out what works best in your location, with your soil and with your average rainfall. We have highly variable soils and highly variable rainfall amounts in various parts of OK, so what works best in an area with plentiful rainfall and well-draining sandy loam might not work best in a different area with dense clay and very low rainfall.