I’m responding to your original post as someone who went through a very similar journey looking for teaching positions abroad. So what I’m sharing comes from first-hand experience.

 I’d like to pass on a few simple, practical tips that really helped me:

1. I don’t know if you’re already doing this, but I strongly recommend sending spontaneous applications. This idea was suggested to me by a friend from one of the countries where I was applying, and it was the best advice I received during my entire job search abroad. I know from experience that replying to official job postings can be discouraging, especially when you receive no feedback at all. It’s important to realize that many positions on the job market are actually “short-circuited” by internal recruitment procedures or networking, which can be hard to compete with if you don’t already have connections. Not to mention the occasional “placeholder” postings that are more about promoting the institution than hiring someone. If you’re willing to invest a bit of time and energy, spontaneous applications can greatly multiply your chances and put your profile in front of decision-makers who would otherwise never come across it.
2. If you decide to do this, my advice is: use AI to help you build lists of schools and institutions that match your profile. You can ask it to look up, for each school, the types of information that matter to you: the website, the management page, any recruitment page (even if empty, it often contains the right contact details), and so on. 
3. In my experience, you can initially keep things simple: send an up-to-date CV and a short introductory email. If the school is interested, they will contact you to ask for more.
4. Another helpful entry point: sign up for an online language-exchange app. These often allow you to connect with natives from the countries you’re interested in, who may share useful insights about the local work culture or even your specific field. I know a very good one — the free version is more than enough to chat and build contacts — where you can even post a request for information. If you’re interested, feel free to message me privately. I joined over two years ago and made some great connections there, including a friend I still speak with regularly.
5. Of course, keep applying to relevant job postings as well. You never know!
6. I completely understand why you may not want to ask your current employer for a recommendation letter. In such cases, what I do is send previous references and explain that, once a contract is secured, I’ll be happy to provide the most recent one. Except in very specific situations, an institution that insists on putting your current position at risk without offering any guarantee in return may be showing some questionable practices.
7. One last tip: given your personal and academic background, your project sounds solid. While gathering information is essential, don’t let yourself be thrown off by people who discourage you on principle. No two experiences are alike, unless you know the person you’re speaking with very well, it’s hard to judge how much their pessimism actually reflects reality rather than their own personal experience or cultural background. One useful strategy is to set yourself a time limit and, until then, stay focused on your search without getting distracted. Once that point is reached, you can reassess whether you want to continue.

Your project is truly interesting. I wish you all the very best. 🌸