I went the route of making my own as well. You can make your own nut if you have the correct tap. I believe it's a 3/8-24 thread size if I remember correctly. I cut out my own square nut using some scrap 3/8 or 5/16 plate I had laying around then drilled out the hole and tapped it.
Classic Parts sells some cage nuts too if you would like to just use them:
https://www.classicparts.com/36-91-Cage-Nut-Assembly-3_8-24/productinfo/37-985/I don't know if they will allow enough movement in the nut for adjusting the door, but you could give it a shot.
Also you mentioned that you are going to cut out the hinge pocket. Is the old cage still there in the way on the inside of the pocket? If not don't make more work for your self, you should be able to drill the spot weld holes in the door pillar and then weld the cage nut on from the outside (cage nut should fit though the hinge pocket opening).
Even if the old cage is still there you can usually see the spot welds from it on the outside and then drill them out. I believe this is what I did, been a while.