Wes,
I have never tried starting seed in compost, I just use the normal seed starting mix. But I know that cucurbits love compost rich soil. Starting them in peat pots is a good idea to avoid disturbing the roots when you plant, but you should cut the pots along the sides when planting so as to allow for the roots to spread, sometimes the peat does not break down and inhibits root growth. This year I will try pots made from coconut fibre. I just hope we get some warmth this year, because there is nothing like eating great melons from your garden, with the exception of course for tomatoes, peppers....etc...
Alex