Concrete cow said
If you are cutting through that is going to take a big deep notch for the waste pipe which is going to get deeper in order to get the required fall over a longish run. This could seriously weaken the joists. Waste pipes should be run to an outside wall parallel to the joists not across them.
I'd be inclined to raise the tray and put a step in outside the shower cubicle as you originally suggested.
I am going to replumb the shower/basin so that they go directly to the waste stack. It will mean removing large amounts of chipboard flooring and cutting through as many joists.
If you are cutting through that is going to take a big deep notch for the waste pipe which is going to get deeper in order to get the required fall over a longish run. This could seriously weaken the joists. Waste pipes should be run to an outside wall parallel to the joists not across them.
I'd be inclined to raise the tray and put a step in outside the shower cubicle as you originally suggested.