Colemj - yes I mean without a bridle. - stopping this movement is what the bridle is all about and why a lot of the wider modern cats have a bridle fitted as part of their normal anchoring system.
Mikereed - sounds like you have a real problem, and you need to try removing the kayaks or try a riding sail.
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"Be wary of strong drink. It can make you shoot at tax collectors - and miss."
Robert A Heinlein
If there is no current , anchor by the stern . It will lay there like a dead duck ,presenting a tiny fraction the windage , and thus a fraction of the load on the anchor , and a fraction the chafe.
You can walk the rode to the stern in calm conditions , and let it off , allowing her to swing head to the wind before uping anchor.
This also works well with a drogue in a storm.