Hopefully to be helpful:
The great difficulty with finding a location for a man in that type of unit is that he was part of the giant supply and transport organisation supporting, in his unit's case, the Corps Heavy Artillery of VIII Corps. That is not one unit but a number of heavy artillery units assigned to provide fire support for the whole of the battle being waged by the infantry and armour across the whole of the Corps front, a matter of some miles. The heavy batteries were themselves some miles to the rear of the line of contact and their supporting siege park (which was found by 593), located ideally near the centre of mass of the artillery units. There were a number of different tasks for the men of the ASC company, he may have been a clerk recording issues of ammunition or a driver delivering the same ammunition up to the guns. Whatever, unlike with Private Smith of the 10th Amesbury Hussars who we can, with the help of a unit war diary, be fairly certain where he was on the day he fell, our ASC man is much more difficult. He could have died as a result of counter battery fire on the Siege Park (ie when the enemy artillery try to knock out your artillery and its support), as a result of an unlucky shell when going about his vital business or, as with another ASC man I looked at recently, simply had a traffic accident which may have been recorded as enemy action.
Actually VIII Corps was 2nd Army. The link by Genechaser to the Battle of the Lys, in which 2nd Army's VIII Corps was engaged to the north of 1st Army, brings you to the area over which the Corps, and hence its artillery, was fighting. The Corps HQ on 14 April 1918 was at a place called Blendecques which may well have been in its centre of operations. The map in the Great War history
https://archive.org/stream/storyofgreatwarh07churuoft#page/292/mode/2up/search/German+Offensiveand the narrative will give you an idea of the area in which Second Army was fighting in (Blendecques is just south of St Omer).
I appreciate you don't have the resources to download a multitude of NA documents but, for the record and in the knowledge that NA say they are in the process of digitising, here is the record for 593 in the period of interest.
http://discovery.nationalarchives.gov.uk/results/r?_st=adv&_dss=range&_ro=any&_p=1900&_q=593+AND+Siege+AND+ParkI wish you luck with your most valuable task, especially as there is a vague possibility that an distant ancestor may be on the Tisbury list, grandmother's grandfather (!) was a Tisbury man.
maxD
Further brief reference
http://www.longlongtrail.co.uk/army/regiments-and-corps/the-army-service-corps-in-the-first-world-war/army-service-corps-mechanical-transport-companiesgo down to "The ASC MT Companies attached to the Royal Garrison Artillery as Ammunition Columns / Parks"
