Taking a page from jewelry fabrication, I wet-sanded the face of the lids on 230 grit silicon carbide sandpaper on a glass table using a circular motion. This gives you a very flat surface.
Now they fit together tightly for welding:
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Prometheus Fusion Perfection 
[…] Previously I tried wet sanding. This worked decently. However, I wasn’t able to get the deeper surface imperfections, it took a lot of sanding. The outer ring of the torus half saw more material removed than the inner ring, which means that the inner rings mate very tightly, but the outer ring has about a 0.25 mm gap. […]
[…] reacts chemically. The magrid part is likely too delicate to be secured for machining. We can still lap sand the faces for better mating. […]