This is probably well-known to more advanced students of both languages, and is so obvious that I feel silly for not noticing it earlier, but if someone told me about this before I had forgotten it.  Armenian seems to have borrowed the root of their words relating to translation (targmanut’yun, targmanich, targmanel) from Arabic or, more likely, Syriac, given the strong cultural and commercial ties between classical/medieval Armenia and Syria.  In Arabic, the word for translation is tarjama, so the connection between that or some variant of it and targmanel is clear enough, since anel means “to do” and the gim in Armenian is equivalent to the jim in Arabic.