So since the "delayed 18 hours" idea has come up in this discussion already, I thought I'd go through what McClellan actually did and what the scope is for acceleration.
The first thing is that I'm going to assume that McClellan actually recieved the Lost Order between 2PM and 3PM on the 13th, as this accords most closely with the information we have.
Of the formations in McClellan's army:
Cavalry
McClellan sent a copy of the Lost Order to Pleasonton ca. 3PM and asked him to verify it with observations from the front.
Scope for acceleration: minimal.
National Road units (main body)
9th Corps
McClellan had already sent the vanguard of 9th Corps forwards, and after the Lost Order was recieved he ordered 9th Corps as a whole forwards. They conducted a night march which was slow but which did happen.
Scope for acceleration: minimal to low. 9th Corps is subsequently sluggish and there's a massive traffic jam in Frederick. If 9th Corps could move faster then it would speed up the whole main body.
There is no 18 hour delay in the movement of 9th Corps.
1st Corps
Ordered to advance at sunrise on the 14th, and wake up hours beforehand (at 3AM) to be ready to march. They move once 9th Corps has cleared the road.
Scope for acceleration: minimal. There is only one road through Braddock Pass.
2nd Corps, 12th Corps, Sykes
These units follow 1st Corps.
Scope for acceleration: moderate,
if there is an alternative route by which they could have bypassed the bottleneck in Frederick and at the Braddock Heights (without using Jefferson Pass as that is earmarked for the 6th Corps column).
The road network in the Frederick area seems to indicate that any such route would be a significant detour.
6th Corps, Couch
Franklin was ordered to advance at 'daybreak' on the 13th,
without waiting for Couch, and to attack ASAP ("half an hour after you hear firing" from the main body's line of advance, is the
less aggressive option given).
This order was sent after the capture of Jefferson Pass, and was timestamped 6:20 PM (so probably reached Franklin after sunset).
Scope for acceleration: moderate.
Franklin could have been ordered to move his whole corps to Jefferson Pass before the pass had actually been taken, but according to the itinerary for 6th Corps their 1st division actually did march to the foot of the Catoctins on the 13th. (No information about the position of the 2nd division is available for that date in the itinerary.)
The order to advance at "daybreak" means that 6th Corps should have begun marching as soon as there was enough light to see. If Franklin did indeed delay for hours after that then that's on him; if he didn't but took about ten hours to get the head of their column from the foot of the Catoctins near Jefferson to Cramptons Gap, then that's potentially problematic.
The other option available is a night march, but this would be fraught with potential risk. When McCellan orders 9th Corps keep moving overnight he has cavalry as far as Middletown and the road the corps column is meant to follow is a single high quality road forming a direct route; 6th Corps is having to follow a comparatively winding country road.
McClellan could have gone over to check that 6th Corps had begun marching at daybreak. However, the unfortunate reality is that he has to sleep at some point, and he was certainly awake at 11PM (when he sent to Halleck about having taken the plans and Catoctin Mountain) and midnight (the telegram to Lincoln).
The fundamental problem with the 18 hours claim
McClellan did not delay 18 hours before moving his troops. His orders had both columns slated to move as soon as practical (with 9th Corps being in motion before he found the Lost Order!) and the only part where a delay can be identified in his orders is if 6th Corps should have been west of the Catoctins before sunrise on the 14th.
The fact that a lot of the "18 hours" in question consist of the middle of the night tends to indicate that it's more of a buzzword than sober analysis. Armies generally can't move 24 hours a day, certainly not on an advance to combat.
The closest thing to a missed opportunity
There is an argument that can be made that the fighting at Cramptons Gap should have begun earlier, and thus that it should have been successfully brought to a conclusion earlier. This might have allowed for the relief of Harpers Ferry.
The requirement for this is that Franklin has not just the head of his column at Cramptons Gap but enough force actually at the gap to take it by some point in the afternoon, and that there is enough time for him to advance in the evening that next morning he can reach (and fight through) McLaws' main force before Miles surrenders Harpers Ferry.
From Cramptons Gap to Sandy Hook is about 8-9 miles. This means that it's about a "day's movement", or that it's going to consume the majority of a day to march down there at normal rates.
This means that if Franklin has taken Cramptons Gap by about 3pm, it's probably (with hindsight) too late. He'd need to get at least a minimum amount of force through the defile formed by the gap before it's safe to advance (as McLaws has over 50% more regiments than him, so if he marches down as a single road column he'll be at risk of being overwhelmed) and Miles surrendered by about 8AM-9AM the next day, giving only 6-8 hours of good light (possibly reduced by the mountains both sides) to get through the Gap and down to Harpers Ferry.
With three hours of fighting at the Gap necessary to take it, this means Franklin needs to be closed up and ready to attack by noon. But Cramptons Gap is about nine miles from Jefferson, and again to attack the Gap Franklin can't just advance his lead regiments as they come off the column of march - he needs to close up, which costs time.
The least painful way for Harpers Ferry to be relieved on the other hand is simple - Miles holds out as long as he said he could. This removes the whole problem as Franklin
had got to the point he was advancing south down the Pleasant Valley on the morning of the 15th, and so Harpers Ferry can be relieved that day.