Where are the settings saved in the Hicon Integra plugin? I have to reload Mach and would prefer not to have to re-enter the settings manually.

They are stored in the machine.ini file located in the respective profile folder. You can copy this file. The Mach4 software also stores backups if you have configured for it.
Alternatively you can package the whole profile easily. I would recommend this method.
Instructions on how to package profile
1.   Open mach4 using the profile you are working with.
2.   On mach4 menu go to Help->Support->Package Current Profile
3.   Save package to desired location.
4.     Import the profile in a new Mach4 Installation