I know green wood is a problem but I've had to steel wool the lathe beds three times in three days. And this is with them coated with the T-9. It's from walnut but it's not even super wet.
T-9 smells just like WD-40 to me.I have tried T9, but went back to my years old can of Johnsons paste wax. T9 works, but too costly for me. John Jordan always sprayed his lathe bed with WD 40. I have never done that, but he was an advocate of using WD 40.
I only use T9 on the lathe bed. When turning I stop often to look at where I'm at. I also keep a hand broom nearby and sweep off the lathe each time I stop. Especially when turning anything wet. Never had an issue with rust or staining. I constantly blow things off with air and clean up. This only works if you are turning for enjoyment and art like I do. It would slow you down appreciably if you are in production mode.I also vote for paste wax.
Maybe add brushing off the lathe bed every time you stop the lathe when turning green wood.