I also had a series 4 watch with a cracked screen. I went on ebay and put a bid on a watch being sold for parts. I got it for $60 ish dollars and then simply replaced the broken screen with the new/used good screen. The hardest part is removing the screens. You need a very thin device or razorblade to remove the screen. IFixit has several videos which show how to remove/install screens as part of a tear down and rebuild. I found that part to be difficult, but very doable.
When buying a used watch being sold for parts, be sure to verify that the screen isn't cracked or badly scratched. I have learned that if you buy a watch that is IC locked, then the seller can show that the screen works.
There are also sights that sale refurbished or new screens. I don't recall what they charge but probably around $100, which is still a lot better than paying the $350 you were quoted.