Recommend me a swivel cleat

The Selden one has a ball raced swivel which seems much more stable under load. The only thing I would say is that the plastic jawed cleats are pretty bad, it's worth buying an alloy jaw cleat from them too and fitting that, you can always then sell the plastic cam cleat or use it somewhere less critical. What doesn't work, I have tried, is to buy their swivel and replace the cleat with a harken one. It doesn't fit. You can modify the swivel slightly to make it fit but there is nothing really wrong with their alloy cleats so that would be my suggestion. The Harken cleat when new is good, but does wear out pretty quickly. 

are on a stupidly small mizzen and a dangly pole downhaul, so loads would be lighter than a jib sheet!

The Standard one used by Contenders is the Ronstan bullseye which very similar to the Harken. It shouldn't do what you describe so I suspect the swivel has become loose as its aged. you may just need to replace it. 

The spinlock does the job very well too and you don't need to uncleat it to pull it further on.  

Is there a better design that will have less play? 

Edit: Video of solution to save new readers from going through all the posts