Annie, personally, I wouldn't worry about it. If you poke around, if you haven't already, you'll find how much I crave re-creating this, and other French alpine makes, in an authentic, traditional way. I really have no other desire, in cheesemaking, than "capturing the ancients," and no pretense to improving on much.
I've had to learn a hard lesson, and that is, to either move to Jura, or shut up, and do my best with what I have. I can't make Beaufort, reblochon, tomme, Mont D'Or; at least not where I am, with the materials - land, milk, indigenous and added flora - I have. But I can learn tons by trying, and what I'm coming up with is pretty darn pleasurable.
So, I'd say, with your jersey, you've got a wonderful resource. You can skim it back, and I'd warrant you'll come up with an extraordinary cheese.