It's an extraordinarily thorny situation, trying to set up what you're talking about. The reason so many gaming sites abroad shut down in recent years, as suggested, had to do with their reliance on US customers. In that sense, the US did "export its (ahem) morals". Morals, lest we forget, are the US's stock in trade -- its most important export after guns, bombs, military aircraft and fast food.
Leaving that aside, though, there is a basic lack of infrastructure (not to mention trust) in most of the places that do allow so-called unlicensed online casinos at this point. If you're in business to make money at it, and this is what you want to do, it's best to regard all national jurisdictions as their own mafias. Each runs its own lotteries and casinos (the US included), and each can and will demolish you if you try to run a game of chance on their street corner without kicking a big chunk of your revenues up to the bosses. This is just the way it is. There's no terra incognita at this point. Short of invading a country and deposing its leaders, you're unlikely to be able to set something like this up without kissing a lot of a** and paying off a lot of corrupt (or "morally upstanding") patriots, wherever you go.
Lots of jurisdictions offer licensing -- quite expensive -- after which you can legally host your site in their country. Do NOT use any host or licensor you find on Google offering supposed turn-key solutions to this problem. They will take your money and run. Slogold, etc. Ignore it; it's not real.
The point of licensing, so-called, is three-fold: 1. To legally incorporate in some jurisdiction where you can host, 2. To therefore be a legitimate corp in the eyes of merchant processors who will not take credit cards or other types of payments on your behalf if you're not legal somewhere, 3. To convince your users that you're not just going to take their money and run.
The prices vary wildly. For around $15,000 / year you can have your site audited, become incorporated and licensed in Curacao, and host your site there. Unfortunately, you'll be hard pressed to find a line over 512 kbps in or out of the island. Costa Rica requires only incorporation, which is cheap, but presents similar bandwidth issues and carries a stigma of zero licensing. Also, most Costa Rican IPs are blacklisted around the world due to a decade or so of heavy abuse. Malta, Gibraltar, the Isle of Man and the Kahnawake reservation are some of the top-notch jurisdictions where fast hosting and decent licensing is available...at a heavy price. Major taxes and starting fees apply.
Put it another way, if you have $500,000 to spend, and applied it wisely, you could probably get a small US state to pass an intrastate online gaming law and give you a lottery license. Crooks, all of them; and they have the gall to claim moral rectitude. Lol.
Good luck, you'll need it; keep poking around though, you might find a loophole somewhere. That's how all the successful ones got started.