At least in China, it's gotten much harder to teach without a degree. In most other countries it's always been very difficult anyway.

In China, they don't really give a wet slap about your education...the real rub is having some kind of shiny, impressive-looking paper they can use to convince the local Labor Bureau and police Exit-Entry Bureau to grant you a Work Permit and Residence Permit. These documents are ABSOLUTELY REQUIRED in order to live and work legally in China; don't ever let anyone convince you otherwise.

Conditions constantly vary with time and place, but TEFL certifications often do the trick, and your Montessori cert might also work. When applying, just be upfront with the school about your qualifications and see if they think they can make it work. A number of folks simply buy diplomas, complete with real-looking transcripts, online and present those; Chinese schools rarely lift a finger to check qualifications. They don't really care and they don't want to know. This practice is of course howlingly unethical, but in China the concept of "ethics" is pretty negotiable (if not disposable) anyway.

If you have sufficient beads and mirrors, you will likely qualify for a Residence Permit and could find a job in China, even at a university or public school.

Expect most other countries to be tougher. China is pretty much at the bottom of the qualifications barrel, at least among countries that any semi-sane person would ever consider living in, and it will be uphill from there. Top of the heap is probably Western Europe, which requires and checks and expects good qualifications...as well as a hard-to-get (by outsiders) EU work permit.

For places with great schools that aren't in Western Europe, North America, or Australia/NewZealand....I dunno, try other planets. Most of the EFL business is the same nasty poo with different sets of flies on it. But...you can support some travel that way. Just don't start taking it seriously.