There's a medal index card at the National Archives web site (poor quality B&W scans from microfilm) at http://www.nationalarchives.gov.uk/records/medal-index-cards...
(scroll down to name input screen) High quality colour scans available on Ancestry.
Corps Regiment No Rank
Royal Highlanders 9916 Private
Royal Highlanders 9916 Serjeant
I can't access the actual cards but the two entries indicate he was a private when he first went overseas and a sergeant when he was discharged or the war ended.
The picture is very small but after enlarging it, I believe the badge on his sleeve is the Lyre that was a bandsman's trade badge. Bandsmen served as regimental stretcher bearers so that supports part of your information. Being a sergeant wouldn't directly equate to him being a drum major and search of the National Archives indicates some 21 men whose rank was actually given as drum major.
Your reference to being awarded "King's Corporal" I assume you mean he gained a field promotion, which was considering the losses in WWI was a common event.
Use his service number to check for any surviving record on Ancestry (all that do exist have digitised in conjunction with the National Archives and placed on Ancestry)