You can say "finalización". You are right, even though the word "terminación" exists in the official Spanish dictionary (RAE), it's not used frequently and even sounds as if it's a "made up" word.
Another thing you could do, as you surely already know, is translate it in a different way, for example:
"Cuando terminaron el Nuevo Testamento..."
"Al momento de finalizar el Nuevo Testamento..."
Sometimes you can't translate certain things literally and exactly as they are written in the original language, so circumvent this by expressing the idea in an equivalent manner. But, in this case, you're in luck, there is an equivalent of "completion", so you can say:
"En el momento de la finalización del Nuevo Testamento..."