John,
Looking at Icom's website, the IC-7850 and IC-7851 appear identical. The latest version of the INI files
on the OmniRig website (dated 2016-03-03) has the IC-7850. Have you tried that?
The INI files are text and are quite easy to modify. There's a list of the supported commands, a program to
validate the rig files and a 'client' program that will actually monitor the interaction.
Dennis recently posted a Youtube video on setting up OmniRig with LOGic.
73's,
Don