I've cut quite a bit of plexi with jigsaws and tablesaws; however, I think the thickness of the material will dictate the best way to cut it. Variable speeds will help. Too slow cracks the material and too fast melts it ( which is better than cracking it) Ideally you will have a piece of scrap to practice with, and if not, I would lean towards too fast inititally. You can buy a reverse tooth cutting blade for the jigsaw, or simply the highest tooth count blade you can find. I had similar results with both. FYI, my cut edge was always face down so cosmetics were not important. All of my cuts were straight, and made on 3/16" material. I would lay blue painters tape across the cut line, then mark out the cut on the tape. Our vendor said that a router was the best tool for the product, but the jigsaw/tablesaw worked just fine for our applications. Should also be noted that our table saw has a dedicated scoring blade. Otherwise, reversing the teeth on the main blade may have been required.
Depending on the cost of the replacement windshield and any new tooling you may have to purchase, you may consider having a plexi shop make your cuts. Most frame shops are also accustomed with cutting plexi.
Post some pics when you get a chance, and that may help with suggestions.