BuOrd looked at several AP projectile designs the mid to late 30s. They looked at a 20% and 40% overweight models. The 20% (4.5 caliber long) for the 16-inch caliber became the 2,700lb Mark 8. They also looked at the 3,050lb (5.0 caliber long) deign and manufactured some test projectiles but few records have survived (or hopefully they just haven’t been found).
It was hoped that this projectile could be fired from the 16-inch/56 Mark 4 but plate battery tests found that its obliquity performance against heavy armor was inferior to the 20% overweight projectile and thus it was obviously not adopted.
I am not aware of a 2,400lb projectile but I haven’t had my nose in the books in some time so there could be one that I am just not recalling.