A friend of mine has set up a simple company in Hong Kong to invoice his remote working for an American employer. He is living in Japan and has a Polish passport. It seems the Japanese authorities don't really seem to care. But I don't know how kosher the whole arrangement is. In any case, Singapore and Hong Kong are worth a look. They are very business-friendly, and you can probably make something work there even le…
I moved to Singapore a decade ago, and I can definitely recommend it. If you'd like to try this, all the relevant visa information is available from the Singapore Ministry of Manpower: http://www.mom.gov.sg/passes-and-permits I think the OP could possibly be able to get the EntrePass, if he sets up a local company in Singapore and makes sure his work is billed to it. Singapore corporate taxes are probably lower than…
The "standard" way would be to incorporate, capitalise the entity with around 40,000 USD, prove that the business will be a business (and not you buying a visa) with letters of intent from prospective customers and a detailed business plan, try and set things up so that you're not the shareholder AND the director AND the visa holder, and then apply for an Employment Pass (EP) under your own business.
That EP will be yours if you have received a high enough salary for the past X months (they ask for your salary history for years), if you have set yourself a high enough salary that you'll need to pay out every month, and - in many cases these days - the Ministry of Manpower (MOM) will probably still ask you for "manpower projections" which I think is a euphemism for "prove to us you'll hire a few locals". Oh yeah, and budget another 3,000 USD or so for the advice from Corporate Service Providers (CSPs) after your initial round of DIY applications get rejected for no reason given. The whole process should take you 6-12 weeks. Whilst a Singaporean applies for a company online for a few dollars and gets it done in a week.
Once you've jumped through those hoops, yes, things are pretty good. Low taxes, extremely efficient government that treats you like a customer, rule of law, low cost of living (compared to Western large cities, not Bangkok or Beijing), great weather, international community, easy travel to dream locations, and so on. I wouldn't want to be anywhere else. But it's not a pain-free process the way say, Hong Kong was before 2014.