This is a tough one. You don't think you'll find a $200 phone as good as your Galaxy S8.
You say $40 screen replacement service? As in someone will replace the screen for you for $40? That price seems very low, so guessing that doesn't include the screen or it's not a service and it's just the screen. Replacing the screen yourself can be a bit of a pain in the butt, but probably doable. But third party screens are definitely a gamble in terms of quality you'll get. I've gotten decent ones and I've gotten probably just as many complete garbage ones (not factoring the ones that were completely dead on arrival). If you want to pay someone to replace the screen, I expect that may cost over $100.
I think it's a hard choice between dealing with the hassles and risks trying to repair an older flagship phone that could still be very good if successful. Versus just throwing in the towel and buying a cheap $200 phone that will be new and defect free, but definitely slower and lower quality.
Not sure I'd really even mess with any phone under $350 (upcoming Pixel 4A rumored to start at this price). So might be worth getting the screen replaced by a professional local shop and paying the $150+ or so it's probably going to cost to get a quality screen with a warranty. Or take a gamble on a $40 DIY eBay replacement screen.