make the place initially an accidental discovery, relatively inacessible for the uninformed- say, surrounded by whacking great icebergs or something- and don’t harp on it too much. Sam Clemens might not like it, everyone else will be fine.
I also really like the winning it in a poker game idea 
Let me elaborate, since I think I might not have been clear enough about some things.
First Here is a map showing the location of Karla and its trading port, Handels-Insel.
The trading island would be completely open to anyone from any country. The trading island would allow the official Ministry of Trade of Karla to do business with foreign merchants. The best weapons, the latest technology, all of that stuff would eventually come to Karla from the trading port, mostly through their own innovations on designs originating elsewhere. Karla will have natural reserves of both gold and iron ore; it would have much to offer. Their navy would be very strong; it would not be easy for someone to just come over there and invade them.
Well, it’s not in the hands of primitive people. The nobility of Karla is not backwards or superstitious - only the peasant class. Most people on Karla would be farmers or fishermen. But the nobility would have access to scientists, they would be tolerant of new scientific ideas, etc. In fact, Karla would be a haven for scientists fleeing European countries, out of fear that their ideas would be declared heretical. The scientists in Karla would not just be patrons of nobility; they would be allowed INTO the nobility. Where else could they enjoy that kind of treatment? The best scientists of the 1600s would have every reason to come to Karla.
And I see no reason why the society of Karla would necessarily evolve just because the nobility and military had access to modern weapons. The two classes would be completely apart.
I am determined to make this work, somehow. I’ve gotten too deep into it at this point to not do so. Keep the suggestions and the constructive criticism coming, because I’m going to do my best to keep some semblance of plausibility to the story.
Up until the end of WWII, the British had the World’s Largest Navy™. If they felt like invading Karla during WWI or earlier, there was bugger all the locals could do about it, unless they had help from someone Big And Powerful. Like France. And The French would need something from Karla to make defending them worth their while…
Have you played BioShock, by any chance?
You’d have a case of “Haves” and “Have Nots”. And there will be someone waiting in the wings to flog the “Have Nots” surplus AK-47s and M-16s.
Or, to put it another way: Sooner or later bootleg copies of Das Kapital, The Wealth of Nations, and Guerilla Warfare would end up on the Island (especially in the modern era), and then… well, you’d have a civil war.
If I might offer a suggestion, how about setting the story in the 1860s, and have the conflict between the “Traditional” Karlanders (still living in the 1620s), the British Empire (who want their Island as a protectorate/coaling station/strategic outpost), The Union (who don’t want the British there) and the Confederacy (who want the Island for themselves to receive arms and supplies from the UK to fight the Union with)- or some variation on that?
You’ve got a meeting of different time periods and attitudes, but with a greater degree of plausibility- not to mention some great conflict!
I like this idea and see nothing impossible about it. How about if it is protected by America? The US gets a naval/airbase on the trading island and favorable trade terms with Karla. Karla remains independent, but is almost like an Indian reservation or Amish community.
I like your 1800s idea but a big part of my story is going to hinge on 1990s popular culture, mass media, and everything that entails. This will not really be a grand story of war and politics like most historical fiction; it will be more than anything about culture shock.
Half of the story will be from the perspective of the American delegation visiting Karla. The other half will be from the perspective of the Karlan delegation visiting America. There will be an introduction chapter giving a brief history of Karla; rather than an encyclopedia-entry style preface, it will be a vivid description of a grand tournament, tilting match and parade, at the royal palace of Karl XXII; historical facts about the kingdom will be interspersed.
I am going for a Harlan Ellison style here - truly, the history of Karla and its politics are a secondary concern. The heart of the story will be the experience of modern America and Karla being introduced to each other in 1991; through the eyes of various people involved in the meeting, and also the reaction of the news-watching American public. HOWEVER I do want to try to maintain a little plausibility if possible.
If not, then fuck it, Karla somehow developed missiles and artillery 200 years ahead of its time, and was never fucked with by the British navy because they were just too strong to mess with.
why does it have to be near north america? It would be a lot more plausible if it was somewhere way more remote. How about Pitcairn Island or St Helena? St Helena is larger and is one of the most isolated locations in the world.
It could also get away with remaining isolated if it was useful as a buffer state before two great powers, thats how Bhutan and Nepal remained independent with no armies, they are useful as a buffer between China and India so Bhutan is in effect protected by the Indian army against Chinese invasion and vice versa.
They aren’t by any chance going to attack the U.S. and accidentally win are they?
The mouse that roared.
I don’t understand why you think there would be such a great culture shock if the Karlanders have already contact with the outside world through trade. Or is your protagonist one of the uneducated peasants?
My first thought was of old Japan, too, which isolated itself from foreigners. But that also shows why it didn’t work: once the US Navy showed up, Japan had to give in. Also, the introduction of guns changed the whole power balance from the trained elite samurai class to mercenaries who could point and shoot.
Besides, Japan was an established insular society with little input for centuries. Your Karlanders come from an entirely different background: European, which means they are used to many opinons and nations.
Any major invention the Karlanders trade in is going to affect their society. If they get more effective farming methods, then they will have either more peasants moving to the city seeking employment, or a bigger supply of soldiers.
Also, if you want them to keep the old-fashioned mindset, then drastic inventions that keep coming will be hard to explain. Compare other nations with lower technology meeting people with higher technology: you run not only into the “higher technology = magic” problem, you also get questions “why does our God(s) not stop the foreigners from beating us in battle? Our god must hate us and punish us, so we should repent, or their god is stronger, so we must convert” (not: they have better technology).
If the Karlanders are enlightened enough to overcome superstitions about these inventions brought in, then they will start thinking about their society, too, and come up with their own inventions.
If the enviroment around people is changing, then people usually change either to adapt to it, or become far more reactionary.
In your map, Karla looks really big. How many people are going to live there? You need quite a lot for a modern industrial society, and a lot of raw materials to build the factories that make the parts for all the stuff that’s needed. But then you change society.
If the Karlanders have to import everything modern, starting with pencils, then you need a lot of gold, and big operation to keep mining it. Look at the trade with China in the 19th century: they had tea, which everybody wanted, they restricted trade to a few ports and select individuals and didn’t take European inventions (to keep their society stable), and only accepted silver as payment. The result? Because the European powers had problems getting enough silver to pay for the trade they wanted, yet still desired the goods, they
got some tea plants (despite the death penalty) and took them to India, to grow them there and
got the Chinese dependent on Opium, leading to the Opium wars.
Or look at how the Whites traded the Indians bad guns and adultered powder for furs, with prices rising all the time.
