Born: 23rd December 1854 Aberdeen, ( I believe) to Peter Murray & Mary Flood
Married: 5th September 1877 (Shotts, Scotland) to Agnes Brown
When you say you believe these to be his date of birth and parents' details, guess the parents' details were also confirmed in his marriage cert?
Dod's confirmation of what his death cert states regarding his personal details seem pretty conclusive with everything else you also have.
Have you got Agnes and children on the 1901 census (can't easily see their entry - thought daughter Mary Ann married 1900?). Assume she would be showing as widowed by now?
Can't see the entry you refer to for William in Shotts for 1891 but is this Agnes with children for that year:
Agnes Murray 29
Mary Ann Murray 12
Thos Murray 3
Christina Brown 18
Address: 33 Paton's Lane, Liff and Benvie, Angus
Monica

Added: William in 1891, is this the one you have for him?
William Murray, 32, coal miner, b. Aberdeenshire
Address: Pender's Row Spittal's Land, Old Monkland