All he had to do was stop writing names for a while after L very publicly announced that he was narrowing the search area. It's his own ego that pushes him to come up with elaborate ways to hide what he's doing as the number of suspects dwindles.

As soon as he learns that you can affect the time and manner of death, he could have made all the rest seem like accidents, spread out over years. Again, it's his own ego that gets in the way; he wants people to know the deaths are connected.