I no longer have my G85, and I never owned the Olympus 75-300mm. I do own the Panasonic 100-300mm f/4-5.6 mark II lens, and while I was shooting stills with the G85, I would often use the 100-300mm on the G85, instead of using it on my Olympus/OM cameras.
Since I don't have the specific gear you asked about, I'm going to mention what I understand to be the best practices.
Generally, the conventional wisdom is that sensor shift stabilization works better than lens based stabilization for normal focal lengths. But for longer focal lengths (like the 75-300mm gives you), the lens stabilization works better than sensor shift stabilization.
Having a camera that can combine both sensor shift stabilization and lens based stabilization works even better (hence when I had it, I used the G85 with the Panasonic 100-300mm). Unfortunately, this is an area where Panasonic and OM/Olympus are not completely inter-changeable. Combined sensor shift + lens stabilization only works if the camera and lens were made by the same company.
Now, your G100 does not have sensor shift stabilization at all, and the 75-300mm does not have lens stabilization. The general rule of thumb is if you don't have stabilization, the shutter speed should be at least the reciprocal of the 35mm equivalent focal length to avoid hand shake issues. Thus, you would want to shoot with the G100 at least at 1/600 of a second (preferably faster) for best results. If you have hand tremors or drink lots of caffeine you might want even faster speeds.
Generally with longer lenses, I use shutter speed priority mode, and I look at what the ISO will be at the lens' longest focal length and dial in the shutter speed based on what I'm shooting (i.e. do I need super fast shutter speeds to freeze the action) and what ISO I'm willing to live with. Even though my OM/Olympus cameras have sensor shift stabilization, I try not to depend on it too much.
The G85 does have sensor shift stabilization, so you might get reasonable results at say 1/125 second instead of going to 1/600.
If you shoot on a rigid tripod or use a motorized gimal, then you don't need stabilization in the camera and/or lens. If you use a monopod to help stabilize the camera, you might not need as much stabilization. There are techniques on how to brace yourself that can also help. In the film era, these were wide spread, but with cameras or lenses having stabilization, they don't get as much press these days. Looking via google, I found: Caroline Maryan: How to brace yourself for slow shots
Note, these stabilization guidelines are only to avoid hand shake issues. Having IS does not deal with subject movement. If your subjects are moving (and you can't pan the camera to match the speed of the object), you need a faster shutter speed, even if your camera/lens has stabilization.