I think I perceive this point differently than you do. As I see it, if Christ's death paid the debt in full for all (as you said above), yet, in spite of that payment, all still do not become saved, I do not think of itself that would qualify Christ to be the Saviour. To be the Saviour - and as the title implies - everyone for whom He has paid the debt, they, and they alone, without exception, must eventually become saved fully and completely, nothing remaining on their part either to obtain or effectuate it - hence the title of Saviour. In addition to the paying of the debt, as Saviour, He also must make it so that those saved can never commit spiritual sin again. This He did by taking them, upon becoming saved, from under the law of sin and death and placing them under the law of life. And because He alone fully achieved and satisfied all of this on our behalf, we can know beyond doubt, that He is truly the Saviour in all of salvation's aspects.