I know this post is too late for Alex but for anyone else interested in the Western Necropolis, the Church of the Latter day Saints had the records I was looking for, plot details for burials 1919-1921 but the dates extend further than that- check their website. I think that is the cheapest way to access Western Necropolis files for the foreseeable future and the files can be ordered to your local centre- worldwide for a relatively small fee.
It was my first visit to the LDS family history centre & I cant recommend it enough. After a few less than helpful exchanges at the Mitchell it was so refreshing to meet lovely people willing to help you find your records. Although you will need to order Western Necropolis files, they also hold a lot of other records on site, so worth a visit!
Also, as the centre I used was in Julian Street Glasgow I could hop foot it up the the cemetery straight afterwards & found my grave...albeit without headstone (a lot are missing or over, a real shame!) but anyway it is located now none the less.