Cut through load bearing to install 3x10 duct?

[lithnights]

I need to extend existing ductwork from the 2nd floor into the attic so it can then drop down into my newly created bathroom. In order to do this, the 3x10" duct would have to go up between the 2x4 studs and through the top double plate and into the attic. I know this isn't ideal but is it possible? My other option would be to have to run the ductwork along the outside wall since 2 of the 4 walls are load bearing and one is not accessible. I have had contractors come in and they agree in their opinion, I only have those 2 options.. unless I build a 4x12 soffit on the wall and thus avoid the double plate.

How bad is it to take a 3"x10" slice out of the bearing wall (only holding up the attic joists though) with no real way to support it?

Thanks

[LazyPup]

Absolutely DO NOT CUT OR NOTCH the header on a load bearing wall. The maximum stress on that member is in the horizontal plane.

A possible solution is to run the duct up near the ceiling then offset it around the header, between the floor joists and up through the ceiling. You could then install a small sheetrock enclosure to conceal it.