The rod is removeable, but only if it's not under tension – removing the strings will not change the nut situation, same with the penetrationg oil. I would NOT recommend to Dremel away some wood if you can Dremel away a bit of a wrench socket's metal

The problem with those trussrods is the weak guidance of the top part of the rod – Mosrite has improved that with a small piece of tube welded to the top bar instead of the hammered hanger that itself will bow at tension. I'll try to post some explaining pix later if you want.
Cheers, Max