It's quite complicated I know that much. I can't help though.

For example a line of dialog in the data may be used in multiple places and changing it in the context of one without knowing about the others can cause it to not make sense anymore, etc.

There are I believe three English versions: SNES/PS1, GBA, and iOS/Android/PC. The last two versions try to keep the spirit of the less accurate and space-limited SNES version while overall doing a more accurate job since they aren't hampered by the limited SNES cartridge space (it takes way more data to store English text than Japanese).

I know I romhacked snes one quite some years ago and had to add my own accentuated characters and pointers ;)
First step for me would be to locate and open in a comprensive way the text files...

Moved thread to FFVI Subforum to help with collaboration.

Thx Saftle! put it in general as I though it would be similar to FFV and maybe someone did before ;)...

As far as I know .qm files are QT Linguist compiled files, and cannot be read, you can just edit the source .ts files.

But in stackoverflow someone mentions "lconvert" that I've been unable to find...
http://stackoverflow.com/questions/32373449/how-can-i-convert-qm-to-ts-file

This might help. It appears lconvert is a part of Qt Utilities: https://fecub.wordpress.com/2015/07/27/some-lesser-known-qt-tools-and-commands/

It's most likely a part of the Qt download: http://www.qt.io/download/

I'm pretty sure the .qm files are only for the launcher/config program. Open it in Notepad++ and you'll only see references to generic QT stuff like printers that clearly isn't part of the game.

The text strings are in the FF6.EXE file, so additional languages aren't likely to happen without patching it.