Our 32 Pearson also 'sails' at anchor. We use 50' of chain followed by 200' of 3 strand nylon which holds well.
Last October, when anchored by the Naval Academy in Annapolis for the boat show, we observed that every boat around us sat still while we visited every boat within swing room. I payed out more rode, from 120' to 200' but found ourselves visiting different boats.
We had pleasant conversations with the other sailors but would have rather met them in a bar than 10' from their boats with the apprehension that we might need to fend off.
I suspect that the other boats were held still by the weight of their all-chain anchor rode which draped directly down over the bow while our nylon flexed tight with each puff. We were the only boat with chain/nylon and the only boat that sailed on the anchor.
Could that be a solution to the swing problem?