So you need help committing corporate espionage? Hmmm lol
You have access to drives you should not, from your work client machine. No need to go after the server. You want remote access though, that can be a problem. It is going through the network perimeter and depending on the companies perimeter security, you may be out of luck. Firewalls are logged. IDS' may be monitoring the perimeter. Right away, this is a project, a lot of logs to wipe, and devices to own to wipe them.
Why not copy the files to a thumb drive while at work? If the access is based on your network login, chances are you are not alone. You are in a group with other people that also have access to this data. You can copy the data from someone else's machine and login, in case the IT staff looks into the access logs. They obviously are not using active log monitoring, otherwise they would have taken action the second you accessed that data you were not supposed to. Do some chair-surfing at lunch-time