Almost all brands of consumer-grade (that's the less expensive ones) mowers are now manufactured by MTD. This means that most of the homeowner-type mowers you purchase now are essentially the same in quality and workmanship because they were all buil...
John Deere is not the company they used to be. I doubt they have a tensioner and if there is it has little, little adjustment. If the belt keeps breaking clean you better bring it in for some warranty work. If it shreds everytime your working it too ...
Just go to hendrensfarmtoys.com and click on games and sports and then billiard accessories. They have wood and graphite John Deere cues. I don't know if they meet your specs but they do sell them. Good luck to ya!