Missionary Methods: John's or Ours?

Nearing the end of his gospel, the beloved disciple writes

^20:30 Jesus performed many other signs in the presence of his disciples, which are not recorded in this book. ³¹ But these are written that you may believe that Jesus is the Messiah, the Son of God, and that by believing you may have life in his name.

Plenty of people take verse 31 as a purpose statement for the whole book, and rightly so.

Yet most popular preaching I've heard on John uses this verse in the following way.
1. John wrote this so you would believe.
2. I know how to get you to believe (runs through five spiritual laws, two ways to live etc)

Yet John didn't write 'Five Spiritual Laws', or 'Two ways to live'.
He wrote John.
with all it's weird bits, with all it's prayers, with all it's concentration on the Jews and Jewish festivals and Temple and comparison to Moses........ so that you would believe.
To miss that is to miss the potential for the actual book to actually bring people to belief