I know a little about this subject, but please don't take anything here as gospel.
Have you ever cooked beef cheeks before? or a leg of mutton for that matter? What you may have notice is that through most of the cooking process, then meat tenses up more and more. With older meat, this is more pronounce, but the effect is exactly the same as cooking your classic beef cheek. You have to cook the meat up until the point the meat "lets go", and releases the tension. With a braised beef cheek, this is around the 3 hour point normally. With mutton, we've had this happen around the 4 hours point.
right up until the "perfect moment", the meat will just be getting more and more tense, so there are no shortcuts I'm afraid.
Having said that, I think countryfile did a piece a few years ago on a farm that was using meat from ex-milking jersey/guernsey cows, and was getting rave reviews. So you're meat should taste fantastic with any luck!
The other thing is, how long was it hung for? 28 days should be a minimum really, but the yanks do have some methods for dry or wet aging pre-butchered carcasses.... It might be worth looking into that, as it will help shorten the cooking times.