The longer you cook peach preserves, the more the peach juice will concentrate and thickens. This is the good news. The bad news is that, it will start to splatter a bit. This cannot be helped, but can be painful and messy if your pan is not deep enough to (mostly) contain the splatters. So, use the largest saucepan as you have. And, maybe wear long sleeves.  It's also important to use a saucepan with a thick, heavy bottom to prevent the peach preserves from burning. I use either a large enameled cast iron dutch oven or an 8-quart stockpot. If you don't have a heavy pan with a thick bottom, you'll just need to be sure and stir your preserves quite frequently to prevent scorching.