none of the tears are on a seam line. There was one on the transom, but that was professionally repaired.
That's good. Should be pretty straightforward then. Be sure to clean all the old glue off and prep the areas really well, and resist the temptation not to let the glue dry long enough. I know I said it before, but follow the directions to the letter. Are you sure the boat is PVC and not hypalon?