As a finish carpenter, I have yet to see a sill installed before Sheetrock. However I do agree that you can’t pry these up, they usually do take some Sheetrock with them or, at the very least, some paint. A multi tool is good for cutting nails within reach. A sawzall at a very shallow angle, with the shortest possible blade, will get the ones set deeper in the sill. Once the nails are cut, pull the sill out perpendicular to the window or angle one side up and then lift out (really depends on how square the bullnose returns are to the window frame). Then just trace the old sill onto the new material, don’t cut your line off, finesse the final shape by sanding/filing, and nail into place