I have done this with a 55ft cat that tacked a lot at anchor and it works really well. Definitely worth a try,You want to use an old sailing ship technique called Anchor under foot.
First anchor normally. Then, drop a second, ridiculously small, anchor vertically off the bow. On my 36 tonne boat, I used a 5 pound dinghy anchor. Toss another 5-10 feet of rode in the water and belay the second rode and relax.
As the boat starts to sail off on one tack, the small anchor is enough to trip things up and cause the boat to tack. Your boat won't stop sailing, but the swing will be reduced to nearly nothing.