Is there anyway in either Atelier Server Explorer and Atelier Explorer to change the order of the Routine list so that it shows the software in both using Date Last Modified Order rather than alphabetically?
I'm not aware of a way to do this directly. But in the case of routines (and classes) shown in Atelier Explorer (AE) these are files on your local filesystem. When I switch to the Project Explorer (PE) view, a right-click on a project gives me an option to "Show in Local Terminal", with a sub-option "Terminal". Choosing this gives me a new Terminal tab in another Eclipse pane. I'm working on Windows, and this Terminal gives me a Windows command shell in the root local directory of my project. There I can issue a suitable DIR command, e.g.
dir /s /o-d
For an equivalent on the server I suggest using Management Portal, which can be quickly launched from the context menu of a connection in the Server Explorer (SE) view. Once in Portal you can use System Explorer\Routines, and click on the Date header to sort the list by last modification date/time.