I've got a problem that I can't figure out.
I'm building a new bathroom upstairs.
The bathroom is up against the back wall of the house and the toilet I need to install would be up against that wall
After taking out the end space for a shower, there is only about 4.5 feet left to put a toilet.
I'm having a problem with how to drain the toilet.
My floor joists are only 2x 8. yet I need to drain with 3 inch pipe minimum.
I do not have any place where I can put the toilet and just drain straight back and down due to a door header that I run into
in the wall below. There are a couple of spots that I can run the pipe down, but that would require boring through
two floor joists, to get to that area
3 5/8 inch holes for the pipe in the 2x 8's is breaking every rule I've found for boring.

I don't think i can run the drain straight back and down due to the header below, and yet I don't think I can run it through the two floor
joists either.

Am I wrong about one or both of those statements?

Is it possible that I could bore those holes in two joist. Would the fact that it's only two joists and that I could do it close to the wall help my case? Could I support those two joists with additional 2x8's on both sides, and then drill through the 3-layered 2x8?

The only other solution I can think of would involve putting the toilet at the end of the bathroom, but that would put the shower in the middle. but the bathroom is tiny. That would be like a "hall shower" with doors on both sides that you'd have to walk through to get to the toilet.

Any ideas or help would be appreciated