I ended up using one piece of 3x4x.250 and splitting it in two:
Fit it in the frame:
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I welded the top in first completely (the white paint is weldable primer, I knew I wouldn't get around to painting it for a bit and didn't want to deal with rust after I cleaned everything). Then removed 6 inch sections at a time from the bottom as I welded it in so that way I knew the frame would flex or move too much:
Then I welded in some L shaped fishplates because I am paranoid:
Take the body off if you have the space. That probably was the worst part.