You've gone the wrong way across the joists, but I don't think it'll be a real problem, and 2 " screws should be fine. The real problem is that you won't have the right amount of loft insulation under the boards, hence why you either use loft legs, or add a 75mm packer to the joists. It's not sure what's aftet the steel rsj, so we can't comment on going further back.