Plumbing through wall that rests on joist

My new construction home had the option of adding a 3rd floor bathroom that I declined at the time, but now would like to pursue. Luckily, the builder already ran plumbing and electrical in the area to easily allow for this to be done in the future.

I already have the bathroom framed and now that I’m looking to get the plumbing rough-in done, I’m realizing some potential issues. My 2×4 walls are framed directly over floor joists, so there’s no way to route the drain pipe up through the wall without eating into a chunk of the floor joist, which I’m assuming could cause issues for me at inspection time.

In hindsight I probably should have used wider framing to allow adequate room for plumbing along where the vanity and toilet will go. Rather than redo this entire wall, I’m wondering if an easier solution might be to essentially frame up a parallel wall with 2x4s, bringing the total wall thickness to 7" which would be more than enough for my plumbing and allow for me to punch into from below without compromising my joist, and similarly avoid the ceiling joists for running my vent pipe.

The bathroom is currently 69" wide so losing 3-1/2" for this is not a big deal. I’m just wondering if this is a proper solution and whether it might raise any eyebrows come inspection time.