No, I'm not rewording your question, I'm reflecting it to show that your question isn't the issue you make it. You asked what was the motivation for the faith to beleive in Christianity without believing that the Bible is inerrant. I asked what would be the motivation for the faith to beleive that the Bible is inerrant.
In short I view your question as a mistake. The belief in inerrancy makes no fundamental difference - I would suggest that the motivations in each case are similar. Arguably the belief in Biblical inerrancy requires more faith to gloss over the internal tensions and inconsistencies in the inerrancy doctrine.