I think that gets to the crux of the issue. Why did Rosecrans leave the Fulton Road open?
1. Rosecrans official claim was that the two roads were too far apart for divided forces to mutually support each other. That's a possibility, but as Grant said in his report, the two roads rapidly converged as they got closer to Iuka.
2. Tony came up with an interesting theory that Rosecrans concentrated his entire force on one road after he learned that he - not Ord - would be initiating the battle. That makes sense too, but if it was true it was in vain, because he found the narrow road limited how much of his force he could deploy in battle. It doesn't help to have a bigger force if you don't have room to use it.
3. The theory that makes most sense to me is that Rosecrans knew he was very late and he was trying to make up time by taking the shortest route into Iuka, with the intention of detaching a force over to the uncovered Fulton road as he came into Iuka. It was a gamble, and it failed.
That's the three theories for leaving the escape route open... the roads were too far apart for mutual support, or Rosecrans realized he would be starting the battle, or Rosecrans had been over-promising his arrival time and was now running very late. In the third theory, as you say, it may have been a sense of urgency that proved fatal to the plan. Simply stopping and assessing the situation, and getting the blocking forces in position on both roads as the sun set, and returning to the plan of a coordinated attack, to be implemented first thing in the morning... may have salvaged the "plan."
Well, we have to recognize what is meant by "rapidly converged." The Jacinto and Fulton roads met the road through Jacinto and Cartersville (the Tuscumbia road, I believe it was known as) around 4 1/2 to 5 miles from one another and converged to within about 1 1/2 miles from one another as they neared Iuka, give or take. The Bay Springs road was quite close to the town, but the existence of which was well known before the operation was put into motion.
The fundamental problem was that it was a race against the clock, as the Army of the West could always pull back to the east via Bear Creek, especially if not substantially pressed. So, as the timetable fell behind and Grant was notified of such, it became problematic in that Grant then elected to withhold the attack and per his account, to actually alter the plan and so inform Rosecrans, or so attempt to inform him, at least to the effect that the Army of the Mississippi would open the attack. Grant's accounts on this vary to some degree on precisely what he attempted to do that way. The trouble is that, first, it is very unclear that any of this was received or understood by Rosecrans, second it
may have resulted in Price being able to respond more sufficiently to the southern threat and finally it proved to be unworkable in that Ord's forces were unable to hear the fighting as it opened, regardless and hence never moved,
which would have still been the case had Rosecrans sent Hamilton's Division via the Fulton Road, as originally planned. So, if Rosecrans
had moved via both roads and the fighting opened on one or on both roads, it isn't like Ord's forces would have then picked up the attack unless for some bizarre reason they would have been able to hear fighting on the Fulton road or on a different section of the Jacinto road/Bay Springs road which they were unable to hear historically in how events actually transpired.
Yet, Rosecrans couldn't stop and simply cover both roads because forces on each road could not support one another and had Price fallen on one or the other with substantial force, prior to them reaching the Bay Springs road, the consequences would have been severe indeed, but
also because he had a duty to support Ord's attacks if they were to go forward
and most importantly if the Army of the West was not hit hard and their ability to pull back via Bear Creek that night greatly impeded, they would simply do so, as the Confederates were fully aware at this point that they were coming, which Rosecrans would have known to be the case as they had been driving back the Confederate pickets that morning and afternoon.
At this point, you see how the situation began to snowball each way, operating with bare minimums in terms of force strength requisite for an operation like this relative to Confederate strength, with responsibilities to one another which had to upheld and honored, the extreme difficulty in effectively and quickly communicating with one another and the constant threat that the Army of the West was always liable to begin pulling back via Bear Creek, which was fundamental in the conception and articulation of the plan.
As I quoted earlier, here is Rosecrans to Grant, first regarding the conception of the plan:
"Hamilton has sent out Mizner with a regiment and all our cavalry, toward Barnett's on the Jacinto and Iuka Roads.
The only thing that we can do to prevent Price's passing through the defiles of Bear Creek east is to push that division on him and follow it with all of Stanley's force while Ross makes a strong demonstration on his front. This is safe for a day or two if we can keep spies from running to Breckinridge and Van Dorn and Price and you can hold your hand against them. I can pursue with my entire force, which, including Du Bois and Danville, will be about 13,000 men of all arms."
And additionally:
"If Price's forces are at Iuka the plan I propose is to move up as close as we can tonight and conceal our movements; Ord to advance from Burnsville, commence the attack, and draw their attention that way, while I move in on the Jacinto and Fulton Roads, massing heavily on the Fulton Road,
and crushing in their left and cutting off their retreat eastward. I propose to leave in ten minutes for Jacinto from whence I will dispatch you by a line of vedettes to Burnsville."
The plan was approved and was set into motion, but there wasn't enough time to ensure that all units were in appropriate positions for launching the operation. Stanley's Division was well out of position and had to first be moved to Jacinto, which took longer than had been optimistically forecast (which I have studied, as well) and again, all the while, the clock was ticking. Also, it has to be remembered, that per his plan, Rosecrans had assigned himself the brutal aspect of this (authorized, of course, by Grant). His forces were to move much further and were responsible for blocking not only the escape routes to the south, but also to make the crushing attack against the Confederate left in order to attempt to interpose themselves between the Army of the West and Bear Creek.
Is just fundamental in its conception. Can't even get a discussion going with people who obstinately reject the record simply because they don't like it. We could discuss the point regarding whether the plan as formulated and proposed properly understood the situation as it existed, but that just was the conception of the plan as it was formulated. 
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