Welcome, Vinny. Now all I gotta do is remember where that other post is so's I can disappear it.
What Mike said.
No way you coulda run that pipe through three joists and still been far enough from one edge or the other of them joists even if the hole had been small enough, which it weren't. Nope, bad plan.
I don't see any real problem with the raised floor idea, aside from the tripping in the middle of he night thingee. I'd try to make the step finish out at about 7 inches rise so's it's more like a normal stair step if I could. There are lots and lots of little lites made just for stairs that you could fit into it as a feature and eliminate the tripping hazard to a large extent.
Not sure what Lonny has against drain pipes supported on the framing. Maybe he was just grouchy that day. Maybe it's for noise control. Dunno. I frequently run pipes of various kinds through framing openings of various kinds and when everything is done I squirt all the holes and where I shim them away from close framing members with a little of that expanding foam stuff. Keeps everything from moving about and prolly dampens the noise a bit. Don't know if Lonny approves of that on accounta he ain't never seen me do it. Hell, prolly violates some code or another.
My opinion; worth price charged.