Thanks all for your prompt and great response!
So, slime is out then, didn't know about alloy corrosion. I planned on taking a repair kit anyway and I'll look for the string type there.
I have researched buying new tyres in Europe or Turkey but it seems the only potentially cheaper than home options come with a greater risk of "fake" brand name tyres, so I don't feel it's wise to risk that.
I checked out the Michelin PR 6's and I'm now thinking they're the way to go.
Although I didn't mention it in my O P, the idea is to head south through Portugal then across toward Istanbul for the 90 day limit, staying as far south as possible to get the best weather through winter. I'm taking camping kit and will probably be doing quite a lot of camping where the weather permits. So, the fact that the PR 6's list "Trail" in their description, and looking at the extra chunkiness of the tread, should I need to access dirt roads or farm tracks, I could probably do that a lot easier on the PR 6 than any other "Touring" tyre I've seen so far.
Of course, the F800 isn't built for off roading at all but the better looking chunky tread could well allow me to access more potential camp spots.
Thanks again all, I came to exactly the right place for sound advice.