Can always rent an electric 3/4" snake from a box store for under $50 I think. Make sure you’re close to the feed point or you’ll be wrestling with sewage-soaked coil. I’d go from the floor drain that is backing up if you don’t have a toilet you can pull right next to it. Goal is to feed it to the sewer main. Scoping is the right answer, but a powered snake rental and an hour of dirty work has a chance of giving you some breathing room.