I am leaving for similar reasons, plus the opportunity to be with a young, untouched woman.
Anywhere in Latin America outside beach resorts and the large cities is going to give you a much more conservative atmosphere.
The problem is where you can get in without a six-figure bank account or a corporate posting.
Paraguay is the easiest to emigrate to. Takes 5 or 6,000 USD (actual figure is in "guaranis") to deposit in a Paraguayan bank, plus a small fee to a "fixer" to process residency applcation. Then you have to stay in country for 2-4 months to complete residence. (Might be faster with a larger gratuity.) Go down there with all documents in order plus FBI clearance letter (i.e. your criminal record) authenticated by State Department or a notary in West Virginia where the FBI is. (This procedure is in flux, just do what you can, and give it a try. Paraguay is not as fussy as some countries). You'll also of course need birth certificate and passport. Take all that to your Paraguayan consulate. Set an appointment and be gracious
to the interviewer.
Uruguay can be done but you have to set up a company and create a steady salary for yourself (unless you have one.) Setting up the company takes a lawyer or "notario", maybe both, plus a CPA to review bank deposit records. Basically you are proving a steady reliable income of around $500 to $1000 a month. (It was $500 but I heard they were going to raise it, maybe still $500).
Basically Uruguay is looking for someone with an income, aimed at retirees. Paraguay is just looking for someone with a bank account. So for you, Paraguay would be easiest. It is also perhaps the most conservative country down there, although I think.
Also, the path to citizenship is easy in both Uruguay and Paraguay once you get residency. That gives you a second passport, and the flexibility to burn your bridges to the U.S., should you so desire at any point down the road (you never know). Also getting citizenship in either country gives you easy access to travel and live in Argentina, Chile, and Brazil too (though not to work).
In either Paraguay or Uruguay, once you have residence, you can work, buy, rent, do business, whatever.
Bolivia could work for you too, I think you need $10,000 to deposit there for a residency visa. Some racial tension between east and west, though. I think the east would be best for a North American starting a family. Like Paraguay, easy to buy guns, btw.
Anyway these are your only options in South America, to my knowledge. Anyplace else will only let you in as a tourist, unless you are a retiree or already have a job. That means you can't legally work or even rent a decent apartment, and the government will make you leave every so often.
In Central America, I know Costa Rica wants to see $1,500 a month. Mexico is similar. And I would think Uruguay would be more advanced and safer than these places - about like southern Italy.
Some folks, especially young like you, do just go to Colombia or wherever they want, and scramble for 30 days (or whatever) as a tourist, looking for a job to qualify and stay. Seems hard to me, since these countries have lots of locals scrambling for work already - but it has been done.
If you're going to try that approach, I think anywhere in Latin America will probably be conservative enough for you to raise a family,
except the main cities.
Personally, *IF* I could get the residency visa, I would try the coffee country in Colombia, below Medellin, like from Manizales to Pereira to Armenia. Great climate, easygoing people (not as "hyper" as folks from Mexico City or Buenos Aires), plus noone is starving, and it has plenty of clean water (at least it's clean in Medellin), plus it's between mountain ranges, so it's safe from nuclear attack and consequent tidal waves (not my biggest worry, but also not impossible). Medellin is not a major city but it's pretty livable. Transport, libraries, wifi, etc.
I hope someone else weighs in here with more ideas. I am quite serious about moving, hence all the research.
Godspeed!