I also don't understand how McClellan planned the strategy for the 14th. According to his order to Franklin, his intent was to break Lee in two, and yet, he only assigns one corps (plus one late-arriving division) to that key task? And the corps he selects is lead by a general who McClellan as slow and having "little energy"? If we are to believe McClellan's order to Franklin, then it's hard not to conclude that he did not give appropriate attention to what should have been the focus of the effort (Crampton's, not Turner's).
It's kind of a question of who else to use, really, given the positions that the corps are actually in and the operational terrain.
Basically you have two ways you can get troops past the Monocacy and the Catoctin passes to South Mountain - the northern route and the southern route.
The northern route is occupied by the troops heading to South Mountain. It's got a bottleneck at Frederick (only one road through town and no parallel route for several miles north or south) and is what most of the corps have converged upon, because Stuart retreated through the town late on September 12 and until that point there could have been Confederates there en masse for all McClellan could know - like there were until DH Hill left on the 11th.
Then there's another bottleneck which is the pass at Braddock Heights. It is, however, the route with the best roads, including the National Road and the Georgetown Pike (which merge at Frederick).
The other route, the southern route, is relatively unconstricted (as in, it's not a massive traffic jam with ~75,000 soldiers trying to fit down a single road) and that's what 6th Corps is taking, but the roads aren't as good, and it leads up to a single mountain pass (Jefferson Pass).
To get extra troops to Cramptons Gap, there are three possible ways to do this.
Way one: divert troops coming through the
northern route.
This means having troops divert south after Braddock Heights (probably turning left at Middletown, between Braddock Heights and South Mountain). This means that you significantly delay the reinforcements for the column that's pressing up against South Mountain; if you divert 1st Corps then you're splitting up Burnside's wing and effectively expecting 9th Corps (which about the same sort of size as 6th Corps) to fight what - per SO 191 - might be Longstreet's whole force
plus DH Hill's division, all of which are apparently at or around Boonsboro. 9th Corps has to handle that fight itself until all of 1st Corps has taken the turn at Middletown and 2nd Corps has come up behind 9th, which is a delay of several hours in the flow of reinforcements at Fox's and Turner's Gaps.
Way two: divert troops
from the northern route
to the southern route.
This means that you have 1st Corps (or whichever other unit) divert once they're through Frederick, and take Jefferson Pass instead. The result of this is that they end up stacked up behind 6th Corps, and can't begin to improve Franklin's situation until all of 6th Corps has arrived and closed up, as that's the earliest the reinforcement corps can provide a benefit. It also, again, means splitting up a wing, either Burnside's or Sumner's.
Way three: add extra troops
to the southern route.
Again, they end up stacked up behind 6th Corps, and either you make the decision on the evening of the 12th (and if so you might actually
avoid SO 191 being found in the first place - the whole reason it was found was that 2nd and 12th Corps were waiting for 9th and 1st to clear Frederick) or you have one of the 2nd/12th Corps detour around to become the tail end of the 6th Corps column.
Anything else means not merely splitting up wings but splitting up corps. As it was, 6th Corps had enough manpower once it had all arrived to take Cramptons Gap, so to make any kind of difference you need the same amount of men closed up
sooner and so any solution that doesn't accelerate that is insufficient.