With most traditional style derailers, where the upper pulley is on a different axis than the top of the cage (and swings up vertically as the cage rotates rearward), shortening the chain can absolutely buy you some room here.
As
Bill Kapaun suggested, put the drivetrain in the big-big configuration to see if you can shorten it some. If you determine that you can indeed remove one inner and outer link pair, then put the drivetrain back in the low gear combination and use a small piece of wire or two small screwdrivers as pictured above to mock up what your derailleur cage and upper pulley will do with that one link pair removed. It may rotate that cage just forward enough to sneak that upper pulley down out of the largest sprocket.
A longer chain will not help in this case -- it will generally make the problem worse. A longer chain allows the cage to pull further rearward, which will cause the upper pulley to ride even higher.
And all of the above, again, assumes a traditional style derailer. This does not apply to some of the Shimano Shadows or SRAMs where the upper pulley is mounted coincident with the upper cage pivot. In that case, the upper pulley does NOT move vertically as the cage swings, and chain length should not have an effect on upper pulley position.