Thanks Josh.
That's very interesting. From my reenactment experience, I do remember a couple of times where, after front rank casualties occurred within the company, the rear rank filemates stepped up into the front rank, filling the gap. However, I think a majority of the time, both ranks dressed to the right, without any rear rank step-ups. Of those rear rank files then left uncovered by front rank files, half of the rear rank files (from the left) stepped to the front and dressed on the rest of the front rank. I can't honestly say this for certain, however. I'm not an officer or file closer, so I can't always tell what is being done in the ranks unless I'm immediately adjacent to it, and even then, my main concern is to make certain I'm not causing any havoc while firing or jostling around while dressing on my rank.
Both methods seem to make sense (Step-Up and Dress-Before-Step-Up), but I think both ranks dressing to the right (before rear rank step-ups) preserves a better semblance of the height order (no need for you to go into that as I'm all too familiar with it - tall to small, from right flank to left). If rear rank filemates step up to the front rank, and the remaining rear rank dresses to the right, there'll inevitably occur situations where the front rank file is significantly taller than the rear rank file. I'd suspect something similar would happen if the company dressed to the left as well.
I don't recall seeing any instruction manuals mention closing ranks during casualties. What manuals or other documents have you found that address this issue?