Hello Qurator,
unfortunately but as far as I know there is no way to get the .cs file from a published template form. When you publish the form, all files are packaged in the .XSN (template) and the code is also packaged in the XSN in the form of a DLL. The code is compiled into a DLL (dynamic link library) and it is packaged inside the template file (XSN) so when you publish the form, the published template already has the code compiled into it. So there´s no source code in a published form at all.
I´m really sorry but you will have to search for the originally saved template with the VSTA project.
Regards,