Improvement ideas.

[EnigmaMe]

Just an idea: Give Kira a one time "Bury the Note" action. Make a long action to hide or "bury" the Deathnote until the next day. Then a long action to retrieve it on subsequent day(s). Kira would still be arrestable if found with IDs leaving it to the assistant to retrieve it before team L completes the investigation. As a bonus it would be consistent with source material.

[Darkfiro]

Only if L get a Fake Id and he will be notified when this id is used to kill him. As it 100% in character for him to use a fake Id with a Criminal that look like him and with a photo that double will die instead.