I hope that this might be useful:
Teachers, unless they have particularly useful qualifications, aren’t as useful to developing countries as they once were. The cost of looking after a westerner would pay the salary of a local teacher many times over. Hence, many missionary orders that do take teachers as volunteers ask them to contribute towards the cost.
However, many missionary orders like to have native English speakers for their overseas seminaries and universities. The problem is they don’t often advertise for teachers, they just tend to recruit by word of mouth (you find a fair number of retired missionaries end up teaching English in seminaries abroad) – so ask around, approach any missionary orders that have offices or members near you (you might not even know they’re there) and have a chat – you’ll be amazed how helpful some of them can be. You find a lot of people spend their time trawling the internet looking for schemes. I find it best just to talk to people. They like recruiting young practising Catholic men because they’re a good influence on the students, especially if they smell a possible vocation! I teach English in a seminary in Africa. I got my job by approaching a member of a missionary order and asking if I could teach in any of their schools or colleges anywhere in the developing world.
There are loads of religious orders dotted about the place where I am so finding a good confessor wasn’t too much trouble and the order that brought me out here are great at keeping me involved in their community life. As for the TLM – pretty much not a chance. I’ve only heard of one in the whole of Africa (the FSSP run a mission in Nigeria). I think in Latin America it is a bit more common.
I would suggest that you do not mention the TLM until they’ve already bought your flight – that’s a no-no in 90% of missionary circles - it’s sad but it’s not the end of the world. To be honest, the thing I struggle with most out here is a poor liturgy and it is something you should probably resign yourself to before you leave for the missions.
I hope at least some of this is helpful.
Best of luck