Below is the correspondence I mentioned regarding Dawson's Regt taking wagons that belonged to Robt M. Jones. This indicates that all or part of the regiment must have taken the road from Ft McCulloch to Doaksville (adjacent to old Ft Towson). It seems likely they would have continued east from Doaksville to the Line Road and then north via Dallas, Ark. to Center Point. There were only a few good roads for troop movements in the Indian Territory so there are not many routes that would be practical for them.
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ORs, Series 1, Vol 13, Page 962-963

HEADQUARTERS DEPARTMENT OF INDIAN TERRITORY,
July 4, 1862.

Major R. C. NEWTON,

Asst. Adjut. General and Chief of Staff; General Hindman's Division:

MAJOR: I am directed by the brigadier-general commanding to lay before Major-General Hindman the following extract from a letter, dated the 1st instant, received by him from Robert M. Jones, one of the most prominent citizens of the Choctaw Nation, and one of the delegates who made the treaty with the Confederate States, and afterward almost entirely fitted out a battalion of Choctaws, toenable it to enter their service. It is as follows:

General, perhaps yon are aware that Colonel Dawson's regiment, when leaving for Little Rock, pressed five of my wagons; but one, after traveling a day or two, broke down, and was left. The others were taken as far as Doaksville. Having them in charge some six days, then turned them off without giving them any discharge to show their time of service; but they were eight days out before they returned to the plantation; that is, four of them. Please inform me if I am to be compensated for this; by whom, &c.

These wagons were in use hauling corn for the troops at this post, which Mr. Jones was furnishing on credit. Colonel Dawson had been allowed to furlough one half his effective men until the 25th of June, to return home and reap the wheat crop. He applied to the general commanding for permission to scud the regimental wagons to convey them home, and was answered that such permission could not be legally given. He sent them, nevertheless, and when unexpectedly ordered to march to Little Rock they had not returned, and the general refused to let him have others in their place, as there were none that could be spared. To supply his needs, caused by his so sending his wagons away with his furloughed men, he, or some officer of the command, seized those of Mr. Jones. The brigadier-general commanding directs me to say that he hopes the regulation prohibiting the impressment of property will be more strictly enforced in this case, for the reason that the offense was committed in the Indian country and the property of an ally was seized. If it is passed over in silence, great discontent will justly be the consequence. If he had known it in time, and could have seized the offender, he would have treated the act as pillaging and marauding, and tried the party by a military commission. And he also directs me to ask that steps may be immediately taken to compensate Mr. Jones, and that information be given that gentleman of any satisfactory action in the premises. His post office is at Doaksville.

I am, very respectfully, yours,

G. A. SCHWARZMAN,

Captain and Assistant Adjutant - General