Any pics? Assuming a plastic insert is left hand because you've seen left hands is bad. I think you might have the wrong Park tool number, Park HCW-4 BB is for older cup and cone type BBs.
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“One morning you wake up, the girl is gone, the bikes are gone, all that's left behind is a pair of old tires and a tube of tubular glue, all squeezed out"
Sugar "Kane" Kowalczyk