This guy got them to fit & I've seen others on this forum manage it.
305/40R22 fits perfect
What offset did you go with?
I've got the 22x10 FR replicas with offset +45mm with 305-35-22's. I think I've got the room to go with the 305-40-22's but mine is an Overland & I don't plan on lowering it.
Would the rubbing be rectified with spacers. You could check that out with your installer.