Solution was found here:
http://serverfault.com/questions/177139/windows-service-cant-access-network-share
"The fact that the machine with the shared drive is not on a domain is where your main problem is. In order to get this to work you will have to configure the Windows Service to run as a specific user, and then you'll have to create an identical user on the remote system with the same password. It might work then.
The problem stems from the fact that in order to log in to a machine not in a domain, you have to log into that machine using an account that exists on that machine. The machine account for something else definitely won't exist on that local machine. By creating an identical user with an identical password, you might be able get the login to work." -sysadmin1138
I created identical accounts on both machines and the service account was able to access the shared drive. Having the servers on the same domain is a better solution, so I'm working towards that, but this will work in the mean time.