After crawling under there and taking a good look at where the frame meets the cross member from behind, I realized that it would be a very bad idea to install the box with no plate re-inforcement of the frame.
I made a cardboard template of the frame going into the crossmember and used it to cut the 5/16" plate. I used the box as a template for the holes and then cut them with a step bit (so much better than a regular bit). I cut 1/2" holes in the plate and 3/4" holes in the outer side of the frame. I welded some 1/2" schedule 80 pipe over the holes in the plate. Then I placed the the plate in position and used it to drill the pilot holes in the other side of the frame (it seemed like the easiest way to locate the holes in the right place. Then I used the step drill bit again to cut the 3/4" holes. I bolted the whole assembly up the with box to test for fit. when I was satisfied that everything fit right, I welded the plate to the frame with everything bolted up, just to make sure everything was positioned correctly.
It seemed like an overwhelming project at first, but once I dove in it only took about 8 hours for the whole conversion.
Thanks to everybody that gave me advice, it really helped. Next up, 60 knuckle swap.