Your class work, grades, and the tests you already have show your preparation. You should of course work hard to get a high score on the TEFL exam. And yes, a low score of course isn’t good, but coleges that are test-optional consider more than test scores. You have to see what each individual school requires.
Yes, LACs are very well-respected and established in the US and you will not be hindered by going to one. In fact, good LACs tend to have very engaged alumni networks and career centers. Many have high percentages of students going into grad school, business school, med school, and so on. I imagine that outside the U.S., there will be a reasonable amount of knowledge about some of the better ones. The link I gave you is a list of national rankings, so you can look and see if it’s well-regarded. Basically, the higher the number, the more likely it is to be well-known.
Right now, we are all just guessing. You need to get concrete answers from schools you are interested in. You need to investigate which test-optional colleges interest you. All highly selective colleges care about how you “fit.” That includes Bowdoin, U Chicago, and Harvard. So figure out what these colleges care about and what they are looking for. If one of them sounds like you, apply.
I certainly wouldn’t break my back and spend tons of money and time trying to take the SAT/ACT in another country, especially not if you are a competitive candidate and there are great colleges that are test-optional. Really, I keep using Harvard as an example, but the acceptance rate is 5%. In reality, it is MUCH MUCH lower for an international. When you consider that a huge proprotion of spots go to athletes and other hooked students, I am guessing the odds are in tenths of a percent. A college like Bowdoin, as my other example, has an acceptance rate of 14%, and far fewer intrrnstional students apply to it. You might well be very attractive to them, and they offer to meet demonstrated financial need. You can google a list of colleges that offer international students financial aid.