I understand what you are saying but I am in some difficulty trying to explain something that isn't a straightforward process and involves trying to find clues in all the records that do exist.
You do need to find out what battalions he served with within each regiment, that will be found, most of the time, on the medal rolls. In his case, we find the medal roll says he was in 8th Battalion N Staffs but doesn't give his Leicester battalion. It does show something interesting worth looking at. A number of Leicesters with adjacent numbers who
may have joined about the same time are transferred to the 8th N Staffs. (The
may is because each battalion ran its own numbering system so, simplistically, Edwin is given 202987 in x battalion while the joining rate in y battalion is different and 202988 is allocated to Bloggs weeks late/earlier so if we find Bloggs record the adjacent numbers only works if they are the same battalion. We need to look also at the 1917 re-numbering,
http://www.longlongtrail.co.uk/soldiers/a-soldiers-life-1914-1918/renumbering-of-the-territorial-force-in-1917/renumbering-the-tf-infantry-in-1917/. 202987 is in the 4th Battalion Leicesters block so tentatively that was his Leicester battalion but only after the 1917 renumbering to be sure.
A number of moves are now possible: are there any service records or Silver War Badge Records or CWGC records for men of the Leicesters with "near numbers".
From the above, the SWB records have a Leicester man with the number 202984 and who enlisted in Feb 1917 so one might think he enlisted very close to Edwin. Not so as other records for the man show that it was a new 1917 number so we can only say they got their new numbers at the same time. So far, given that Edwin has no earlier number in the Leicesters on his card, perhaps he enlisted in March 1917. ASgain that doesn't work because only the meadl card only has info about the overseas service and he could, for example, have joined in 1916 with number xyx, been renumbered that then gone overseas. Drawing a blank so far.
Next would be a search to find clues to an influx of men from the Leicesters to the 8th N Staffs. The 2/4th Battalion Leicesters were reduced to cadre strength in May 1918, perhaps he moved to the N Staffs then. Over to the war diaries. While both battalion's diaries show men leaving and coming at about the same time (Feb-May 18), I find no specific mention of Leicesters to N Staffs.
At this stage I begin to flag. If this all looks like thrashing around in all directions that is exacty what it is, hopng that a clue will appear somewhere that can be stood up as fact.
As you know, there are some knowledgeable folk on here who may turn up and give you a clearer steer, what none of them will do, I venture to suggest, is say - follow these two steps and all will be revealed, there are simply too many variables.
I must admit to not being able to give you dates for his enlistment/transfer, dates that is that I can
prove. I await with interest to see if others can suggest other ways of solving the puzzle.
MaxD
I am leaving this post as it is having seen jim1's post which you can see is treading the same path as I am!