It's usually risky to send long, unsolicited letters to the Court seeking relief, particularly with extensive argument. Generally you are well served to keep letters short and limited or you may annoy the Court.
The Court frequently says that it prefers parties to make requests for relief by motion rather than letter. This is even included most (maybe all) of the judges' form scheduling orders:
Applications by Motion. Except as otherwise specified herein, any application to the Court shall be by written motion. Any non-dispositive motion should contain the statement required by Local Rule 7.1.1 [that the parties have verbally met-and-conferred with local counsel on the line].
But the Court doesn't always enforce this. It's not …