In time, this will be resolved one way or another and I'm sure that it won't be at the expense of people needing to leave the country. If the consul can't sort this mess out, and they should be able to considering there are something like 500,000 Turkish Nationals enjoying NHS cover in the UK. It may take one or two enterprising insurance companies to pick up the opportunity and run with it. When I was working for a medium sized company in the UK, we put out to tender for private health cover for our 500 employees, each company responded with a clause in their offer that would exclude previously known medical conditions, after a little bit of negotiation one of the insurers offered to drop this condition and soon most of the others followed suit.
Making it financially viable for a company to offer cover, especially to an older and ageing set of members depends on the numbers of people in the scheme, if 10 different insurers try to do it then it will never work, however if one or two companies can do so then there is a ready made market of some 50,000 UK expats and god knows how many German, Dutch & Russians who must be also in a similar position with SGK.
I'd be happy to go and talk to Axa if anyone thinks it's a good idea?