I recently found this additional OR dispatch which adds specificity to dates when men from Price's army retreated through Doaksville/Ft. Towson.
41-4-1059 on 11-17-64 MG S.B. Maxey at Fort Towson writes to BG Boggs at Shreveport:
“Price’s men have been arriving here for four or five days, singly, in squads, and every way. Their horses are miserably poor, as they say, and many are being abandoned on the prairies.”
{Thus, Maxey notes that many of Price's men have been arriving at Doaksville from November 12th - 17th. Thus, these men could have only come from Cabell's and Slemmons' brigades of Fagan's division, which either fled or were furloughed from Price's army between November 8 and 10. Others could have passed Doaksville after the 17th.}
The possibility that some of the early departures could have been deserters comes from:
41-4-1059 Capt. R. M. Marston, who has been sent by BG Cooper with a Flag of Truce to Ft. Smith, during his return writes to BG Cooper on 11-10-64 from 8 miles (southwest?) of Skullyville (Skullyville is 16 miles west of Ft. Smith) the following:
"32 of Price's men passed by my rear guard yesterday."
{Marston believes that these 32 men (seen on the 9th at least a day away from Price's crossing) may be deserters so he sends out a squad to stop them, but to no avail. Thus, some of Price's men were leaving his army by the 8th, one way or the other, shortly after crossing the Arkansas River.}