I also have strong doubts about qualifying for FEIE in your situation. Before I'd seriously contemplate claiming FEIE in this situation, I'd consult an accountant or attorney who specializes in taxes for expats.
As others have said, one of the requirements is that your tax home be in a foreign country throughout your period of physical presence or bona fide residence. I suppose you would attempt to qualify as an 'itinerant' due to your web-based business (IRS Pub 54: "If you have neither a regular or main place of business nor a place where you regularly live, you are considered an itinerant and your tax home is wherever you work."), and thus you would claim that your tax home moved with you from country to country.
However, Pub 54 also says "You are not considered to have a tax home in a foreign country for any period in which your abode is in the United States. ... “Abode” has been variously defined as one's home, habitation, residence, domicile, or place of dwelling. It does not mean your principal place of business. “Abode” has a domestic rather than a vocational meaning and does not mean the same as “tax home.” The location of your abode often will depend on where you maintain your economic, family, and personal ties."
If you are a pure tourist hopping from country to country for 330 days of the year, I suspect the IRS would say your "economic, family, and personal ties" ultimately point back to the US. That could be true even if you don't have a property back in the US.
BTW, you said your business is bringing in 60-80k/year. After taking advantage of business expense deductions and HSA/401k contributions, isn't your taxable income, and thus your ultimate tax bill, extremely low already?