My Latex 310 is reading that the maintenance cartridge is ok, but I want to replace it because I'm having issues with colors appearing muddy. There is a ton of yellow and green ink splattered all over the top of the maintenance cartridge somehow. When I follow the steps to replace it, it says to open the door. The cartridge comes out a bit, but then it goes right back in and says to close the maintenance cartridge door. It doesn't allow me to remove the cartridge. Is it possible to manually remove it without causing damage to the printer?

If you shut down the printer then the maintenance cartridge can be manually removed, to be safe you can push the carriage to the side before pulling it out. Don't do it with the printer running. The maintenance cartridge shouldn't be effecting the printheads to that extent. How much ink has been fired through the printheads? These HP printheads aren't very trust worthy and can go bad at moments notice. So I would try replacing the printheads also.