Though it would ruin the threads on the cross threaded cup, I would try to fit a 12" pipe wrench on the protruding threaded section and remove the cup. Might not be enough to grab, but that would be my first attempt. I have done it before on a bottom bracket and very hard to remove freewheel hub. The bb cup was shot, once removed, the the hardened freewheel hub was still useable.
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"98% of the bikes I buy are projects".