" However, the following month, the brigade, and Galleghan's battalion with it, was transferred to the 8th Division" you may be able to eliminate some of the commas with something like "the brigade, and Galleghan's battalion with it, was transferred the following month to the 8th Division"
"Galleghan was disappointed to find that despite being the most senior of the battalion commanders in the brigade, Lieutenant Colonel
Duncan Maxwell was to be the replacement." could read as either Galleghan or Maxwell was the most senior
" was withdrawn to the rear by a pessimistic Maxwell." maybe specify either why Maxwell was pessimistic, what he was pessimistic about, or why it's relevant
" However, the following month, the brigade, and Galleghan's battalion with it, was transferred to the 8th Division" you may be able to eliminate some of the commas with something like "the brigade, and Galleghan's battalion with it, was transferred the following month to the 8th Division"
"Galleghan was disappointed to find that despite being the most senior of the battalion commanders in the brigade, Lieutenant Colonel
Duncan Maxwell was to be the replacement." could read as either Galleghan or Maxwell was the most senior
" was withdrawn to the rear by a pessimistic Maxwell." maybe specify either why Maxwell was pessimistic, what he was pessimistic about, or why it's relevant