Having a tensioner would just be a band-aid, as was pointed out earlier, wear on the sprockets (and noise) would be the trade off for a few more miles. Either of my high mileage vehicles have had this issue (YET!
and my wife's E83 transfer case had only an ounce or two of oil in when we bought it. Not only is the hydraulic pressure of the oil on the chain a problem, if the clutches don't have the right coefficient of friction, maybe some different size/wear issues on the tires, that all adds to it.
Try replacing the gear lube in your snowmobile chain case with low temp lubriplate and you be shocked at the difference it makes