The incoming structure doesn't make sense for the live Revit files. Here is the reason:
Most projects should be using central files. The moment you download a model from your clients/consultants and place it in an incoming\<date> folder, it is really a local file looking for the central file from the original location.
Therefore, you must open the downloaded file Detached from Central (DFC), and save it to the real location. "Real" is whereever you want it, but as you have seen, linking into variable folders or using variable file names makes no sense whatsoever in Revit linked projects.
Especially when you consider that you must open all outside central files DFC. So why not just save them as central files in the same folder as your own models and give them your own filename standard? Of course that filename standard should not include a date or other variable.
Another consideration is that renaming linked models will break copy/monitor operations.
So our firm has adopted a flat folder for the live models and we use our own filename standard even on the client/consultant models. We still have an Updates folder where we store historical models, but those are the direct downloads that need to be opened DFC and saved to the flat project folder as the real central files.
I hope that helps.