Self-Employment

They are going to want to know your source of income to make sure you are not a burden on the country.  If you are internet based you are not a business in their country so that's not a problem (I have two companies, both internet based, and I live in Panama but sell to American's mostly).  I just need a good internet connection.

Have you visited Uruguay?  Do you know what area you want to live in? 

There is a group of expats who meet every Sunday in Montevideo.  Some of them have been in the country over 10 years.  We met with them when we visited the country last year.  Uruguay was one of the places we thought about moving too.  Still an option actually.  I was offered a job by a local which would help with residency tremendously.  To get your residency you have to invest quite a bit of money, or buy property in the $100,000 range.  There are ways to get residency but just operating via internet isn't it.

The bigger issue is renting.  Make sure you find someone who is reputable and who is really able to rent you a place.  And if you can pay 6 months of rent in advance you might have an easier time renting. 

Beautiful country.  Enjoy it.