Bathroom remodel.. exterior-facing wall significantly not plumb!

[whitej125]

My wife and I are renovating one of the two bathrooms in our 1950's cape code style house. We tore down everything to the studs and sub-floor. In doing so we noticed the single exterior wall was significantly out of plumb. From sub-floor to ceiling joist (90")... the wall tilts out 2.5" at the top. I do not any signs of settling... it almost looks like this was the way it was built. The other rooms on the second floor have the same issue, but its all painted... so you'd never notice it and there are no cracks.

With painted walls in most of the room... you wouldn't notice the imperfection. But we are installing a new tub and tile in the alcove who's back wall (opposite side of the tub as the drain) is this exterior wall. Not only are we going to have issues putting in the tub... but that rear corner where subway tile meets subway tile will look weird. How can I work around this?

My thoughts so far...
1) Leave it and live with the tile looking misaligned in that corner
2) Somehow create a 90" long shim to nail into the exterior studs to compensate for the wall tilt along the bathtub portion only (thus making the tub surround plumb and square) and somehow transition that to the rest of the wall.
3) Same shim idea... but do it for the entire exterior wall (could interfere with the window?).
4) Something involving lots of plaster?

Thoughts?