The "analysis" so far shows that the men who serve on the West Coast of Africa in 1873/4 had Corps Numbers between 1032 and 3628.
The lowest number I have so far found for a man who was a transfer from a combat corps was 1630 Henry PARSONS, who joined the "ASC" on 1 April 1869 from 15th Hussars
However, James WAGER- the chap you were interested in before - was ex-CTC serving in New Zealand (having been 81st foot before then) and his Corps No was 1786
All the chaps with Nos 1287 to 1891 appear to be in alphabetical order, thus if the Corps No system was introduced towards the end of 1869 after the promulgation of the Royal Warrant, it may be assumed that they were all serving with a predecessor unit, even if, like Parsons, they had only recently joined (it would be easier to sort them alphabetically than when they first joined a predecessor unit; after all, which unit would take precedence?). The handful of men with numbers between 1032 and 1164 were senior NCOs and may have been treated differently
The names of the men with Nos 1900 onwards are alphabetically random, so presumably each number was issued on joining the ASC - not when they were officially transferred, but when the started their up-to-3-months probation.
I say that because there were a number of men transferred to ASC on 1 November 1872 - of those known to have been transferred on that date, the lowest number (3235) went to Thomas SWAINE (ex 68th) and the highest (3405) to John CONCHIE (ex 64th). In total, there were 10 men who served in the Ashanti campaign with numbers between 3235 and 3405, of which five are known to have transferred on 1 November, and I presume the other 5 did as well.
I am now extending The Project to see if I can find other men with Corps Nos between 3235 an 3405 who may have served in South Africa or Egypt and, if their records survive, the date on which they transferred, to confirm my idea.
I was wondering how you found out all the information about Corporal Hills? I have his medal and when I went to research it, I could not find his service papers at the NA.
Hills' records appear on Ancestry in their 1914-1920 British Army Service Records database - which is where I've found such other records as I have been able to quote (except GGFather's, whose were in the correct place in Kew). If you don't have access to Ancestry, just let me know.
In order to research all these men on Ancestry, I created a public tree, which has meant that a few people have contacted me because I have added one of their relations to that tree - including Corporal Hills' grandson, who told me that Corporal Hills: "was a founder member of the St Pauls Masonic Lodge, Limmassol who evidently arranged for his burial and headstone"
I'm (hopefully) attaching a picture of the headstone which his grandson recently had restored. I am sure his family would like to know what happened to his medal and you might be able to get more info from his grandson, so if you would like, I can see if I can put you two in contact