That is an interesting story about the pension file. I would love to see the original documents from that case.
You are correct in imagining that the practice of executions was not tightly regulated. Many officers displayed little knowledge of military law and paid scant attention to "technicalities". Hence we see cases like Colonel Michael Lawler of the 18th Illinois Infantry Regiment (he allowed a company commander to hang a private for murder after a hasty, unauthorized regimental court-martial). Lawler was tried by court-martial for this action among others but Halleck had to void the conviction for multiple irregularities. No officer of the Union Army was ever dismissed or sent to prison for killing a private in his unit.
As for the pace of executions, consider this. There were only four recorded executions for desertions before 1863 (2 in 1861, 2 in 1862 out of 21 in total, for all offenses) Commanders were reluctant to order or recommend executions. In 1863, executions for desertions explode after the debacle at Chancellorsville. In this year, 54 executions for desertions take place, out of 67 in total. Many of these executions occur in the Army of the Potomac and the numbers continue at a high level into 1864 (57 executions for desertion out of 94 in total. In 1865 there are about 33 executions for desertion before they finally stop in July.
You are also correct in presuming that some officers were more prone to ordering or recommending executions than others. McClellan only approved one. I have not been able to determine if Grant ever approved any, but he followed a consistent practice of simply referring all capital cases to the President for final disposition even when not legally required to do so. Meade however was a different story. He was a strong proponent of executing deserters and complained whenever Lincoln granted clemency to one. Meade probably ordered or recommended more executions for desertion than any other Union general. Douglas Haig would have approved of his disciplinary style.