"cutworms" ... soil-dwelling insect larvae that emerge at night to look for food.

Place a guard around the plant - embedded in the soil on one end and a couple of inches high. A ring of folded newspaper will work, so does a plastic cup with the bottom cut off, or a ring cut from a milk carton.

When the stems are thickened, remove the guard

Aluminum foil is what I use. easier to use and get the size you want. overlap it and the stem will pull it open with growth

You can still plant seeds. I find plants grown directly from seed tend to be less susceptible to cutworms, although I have no absolute evidence of this.

Melons don't much like transplanting anyway.