The two sentences that begin " Previous to this....." aren't quite right. The Infantry had the bulk of the Labour Battalions, Infatry Works Companies and and Labour Companies which although they carried a regimental title, didn't "belong" to that unit and worked under a Regional Command in UK initially. The RA did not have labour units per se. The ASC did have ASC Labour Companies and the RE had Labour Battalions, these were converted to Labour Corps in June 1917.
No real quarrel with the rest of it. However I would expect to see a Labour Corps number in his record and I still haven't found a medal record with the number you gave earlier.
The above is too simplistic for words, I'd recommend No Labour No Battle by Lee and Starling for the full picture.
MaxD