By Alex West & S P Jones Now that Alec Baldwin is being charged for the second time with involuntary manslaughter, the court process is moving quick as he flexes his right to a speedy trial. Prosecutors in New Mexico first kicked off the new proceedings for the same shooting on the Rust set when they filed paperwork on Dec. 31. By Jan. 19, the actor was indicted before a grand jury as prosecutors came in with new evidence and experts to weigh in on the previously dropped case. According to documents obtained by The Mirror, the next order of business is Alec’s arraignment hearing. It’s schedule…