Many years ago we had a problem in our sheep breeding programme with lambs born with excessive wool, about two inches long. They were usually twins and one was always often much larger than the other. They were always poor doers, and very vulnerable to stormy weather at birth but eventually they lost their "Hairy" appearance and always were sent off to the meat packers with the last of the seasons crop.
It was a widespread problem with up to one per cent occuring and many ideas were put forward from mineral deficiencies to bloodlines of base stock.
Using Blackface rams was supposed to be the cure. This improved the situation. It didnt cure it and the blackface ram sellers did better than others for a year or two but somehow we still had to produce white faced ewes as replacements.
Finally most people adopted the policy of culling or putting any ewe that had one of those lambs into a "non replacement" flockand mating them with a blackface ram.
We identified 30 ewes out of 1500 and the problem disappeared.
Would similar policies work for your Rat Tail problems.