Trouble removing Hotpoint agitator spline insert

Anyone have any tips on getting the old chewed up agitator splines out of what I believe is a late 70's or early 80's vintage Hotpoint washer? I cut out the center of the plastic exposing the top of the spline insert but have been unsuccessful driving the old chewed up splines. I've been trying it by putting the agitator on a large piece of plywood and using a socket as a driver. So far nothing is budging. I assume I should only be driving out the center ring?
Thanks for any assistance.

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