To me it doesn't look cockeyed. The loose plate is at an angle to the shaft and coupler. It looks dry, so some sort of lube or penetrant could help.
I've been using a method suggested on one of the tractor boards for loosening seized threaded parts for the past few years that may work for you. Heat the parts just to the point you can't touch them - not even near red hot. Then hold wax against the joint of the parts and allow it to wick in for a minute or so before trying to loosen them. Beeswax (toilet seal ring) seems to work better than candles for me.
The first time I tried it was while removing a cast aluminum fan blade that had steel set screws and was on a steel shaft. It was in a chicken house, so the atmosphere wasn't one that helped preserve metals. Since then a number of stuck nuts, a glad hand on an old flatbed trailer and other stuff yielded to the melted wax.
I used this method again recently and was able to remove all 20 nuts from the (headless) bolts holding the wheel halves together on the RFM I restored.
