I would frame things a little differently. Light makes a lot of mistakes because the Death note is incredibly powerful and there would be almost no reasonable way for L to catch Light without Light making obvious mistakes (and would also make for a boring story). Undoubtedly, the biggest mistake Light makes is revealing the existence of the Death Note, and all the rules therein, which not only gives L (almost) all the information he needs, but also traps him from any subsequent activity.

Without knowing the rules of the Death Note, I don't think L could have done anything (besides outright abducting/murdering Light) to stop Light, even if he is 100% sure Light is "responsible".

That said, I feel like a much simpler solution than what's proposed at the end of the essay is:

1. Gather up the names you want to write over the course of a week. 2. Wait another week, then write it at a specific point of time of the week. 3. Keep to that schedule.

The names need to be as public and as well known as possible such that it would be impossible to trace the flow of information. (Remember, the goal is fear, not specificity.) Keeping to that schedule means you will never leak more information thereafter.