Offline Access cache process is divided into two parts:
1. Priority requests – An example will be when you select a message in Outlook. This takes priority over the backfill operation. Front end server for SourceOne will sort out the priority. There are two ports default TCP ports 8001 and 8002 where these requests are divided.
2. Backfill – This is below above mentioned requests. This happens behind the scenes and low priority. This will also help in situations where all of a sudden large amount of users or emails started to get shortcut. I am not sure if users are on the same subnet where SourceOne server is or they are on remote locations. If they are on the remote location then backfill might be time consuming and it would help to have machined available on the same local network where SourceOne is located. Another thing comes to mind is to have a policy where initially only first few months are cached which usually most of the users are trying to accesss. Any cache miss will be fetched on request. Then gracefully increase the time frame.
Usually one should already have offline access rolled out before messages are shortcutted. This way messages will already be in cache before they are even shortcutted by SourceOne. This might not help in your situation though because messages are being archived, moved to mailbox and shortcutted in one job.
It might also help to divide load between the servers in case you are ingesting many PST quickly into systems because all of sudden all requests are going to server for creating cache. What else you can check is how SOurceOne behaves when you try to export large chunk of messages out of it. Depending upong what is at the backend is also going to be a deciding factor.