I think your scenario is far too chicken and egg. I can't imagine how any AnCap society could 'appear' in isolation like that. It is like imagining a ball of string and then imagining an section of that ball not having string. But a ball of string can only ever be unravelled as a ball...... or, if you took a knife to it and cut out a section (like an orange segment) the ball would mostly unravel all around the hole. This is what I think would happen if an AnCap society suddenly 'appeared' out of nowhere.
I think you are forgetting that AnCap is not just a system - it's a set of very powerful ideas and possibilities. If AnCap was known to be actually working in Britain then that would be proof to the German people that those ideas and possibilities worked and existed not far away. Wouldn't Germany's tyrannical hierarchy - born of fear mongering, racist, xenophobic propaganda - immediately start to crumble as its population (including soldiers and government employees) learned of Britain's AnCap society?
Even Göring admitted that: "Why, of course, the people don't want war. Why would some poor slob on a farm want to risk his life in a war when the best that he can get out of it is to come back to his farm in one piece. Naturally, the common people don't want war; neither in Russia nor in England nor in America, nor for that matter in Germany. That is understood. But, after all, it is the leaders of the country who determine the policy and it is always a simple matter to drag the people along, whether it is a democracy or a fascist dictatorship or a Parliament or a Communist dictatorship..../..... voice or no voice, the people can always be brought to the bidding of the leaders. That is easy. All you have to do is tell them they are being attacked and denounce the pacifists for lack of patriotism and exposing the country to danger. It works the same way in any country."
A functioning AnCap 'nation', and all that that implies, just across the channel is the very opposite of the kind of propaganda and oppression which kept millions of Germans following orders.
Statism might have to be imposed by force, but you seem to assume that AnCap (or more to the point: freedom) would also have to be imposed by force. But isn't it more accurate to say that people choose to 'buy into AnCap / freedom freely' whereas we have to be 'sold statism/ tyranny by force'. Perhaps a leaflet drop of postcards from Britain would be all that's required for enough German people to freely buy into the idea of AnCap (and freedom generally) and for Nazi Germany to crumble and the Holocaust be averted?
After all 99% of people are caught up in a war. Nazi Germany was no different. Offer them the possibility of a way out (a clear example of how peace and freedom can be enjoyed) and they will choose it.