There is enough thread visible in the cut outs to verify the thread direction. From here it appears to be left hand. Make sure before beating on it. Use a heavier hammer and a sturdier punch.
Warm the alloy spider with a torch or heat gun and quench it with penetrating oil or water and let cool. If it does not free up easily, repeat.
A local shop does repairs to lock components for the Erie canal. Some of the parts come in with hardware barely recognizable do to the rust encrustation. Some of the parts have been repeatedly submerged a hundred years. The main man showed me once how he deals with them. Heating the parts and water quench till cool is all it takes. Never even needs oil. It may take a few rounds, but the nuts spin on and off by hand with this simple treatment. Water dissolves rust better than oil and penetrates very well.