There are other things you can use unripe peaches for. I've tried a variation of "goreng pisang" with peaches instead of banana. It does sweeten a bit as the sugars caramelize, but not a great amount as not all the sugars have formed yet. Some "puddings" work nicely with unripe peaches.... if you get them at the right time, dehydrated peach slices make a nice snack.

Overripe (soft) peaches is a bit different for me. If I have enough, I'll usually make a simple jam with them. Chunk up the peaches, take 90% and run them through a blender, add a bit of sugar and some gelatin (or agar agar) and let it set. Peach jam.