There's got to be ways and means to make money through more sympathetic farming methods.
I guess at the moment with the small margins in mainstream commercial methods and subsidies for things like preserving natural habitat then there perhaps isn't the incentive to gamble on doing anything too out of the ordinary, if you're getting by and you know that situation is likely to continue indefinitely then why risk it all on something that might not work out? If however the situation starts to look more bleak, as I'm sure as loss of EU money would, then perhaps that gamble becomes more compelling? If you know it's all likely to come crashing down around you in coming years then do you take the plunge with your last few years of profit to try and make a go of something different while there is still a little bit of cash to spend rather than just let it all slowly crumble away to nothing.
Could you do something with game perhaps? Reared in a more natural environment, obviously a much smaller market for it than commercial livestock but perhaps costs are significantly lower too with less intensive land management required, something like deer could perhaps attract a tourist-y side income opening up some of the land for the public, hunting (not that I'm really a fan of it) could also be another income stream if you went down that route and may provide a double benefit in saving costs at the abattoir?
It's difficult but there has to be some way to both preserve land in a more natural state and reap some sort of usefulness from it.