First, those two cameras use different sensor sizes so their focal lengths are not comparable. The G7 uses a four-thirds sensor which is roughly half the size of 35mm film (which is actually 24x36mm) and yields a 2.1x focal multiplier (frequently rounded down to 2x by marketing). The 77D uses an APS-C sensor which yields a 1.61x focal multiplier (rounded down to 1.6x by marketing). So the focal length range you've listed is not comparable.
■10mm on the G7 is equivalent to 21mm on full frame. 10mm on the 77D is equivalent to 16mm on full frame.
■17mm on the G7 is equivalent to 36mm on full frame. 17mm on the 77D is equivalent to 27mm on full frame.
Or put another way
■10-17mm on the G7 is equivalent to 13-22.5mm on the 77D.
■10-17mm on the 77D is equivalen tto 7.6-13mm on the G7.
Second, you're splitting hairs with respect to aperture.
■f/1.4 to f/2.0 is a full stop. A 1/60 sec exposure at f/1.4 becomes 1/30 sec at f/2.0.
■f/1.7 to f/1.8 is 0.12 stops. A 1/60 sec exposure at f/1.7 becomes 1/54 sec at f/1.8.
■f/1.4 to f/1.7 is 0.47 stops. A 1/60 sec exposure at f/1.4 becomes 1/41 sec at f/1.7.
■f/1.4 to f/1.8 is 0.65 stops. A 1/60 sec exposure at f/1.4 becomes 1/36 sec at f/1.8.
So there's very little difference between f/1.7 and f/1.8, and you're eliminating a lot of good f/1.8 lenses by arbitrarily setting f/1.7 as your limit. If you're serious about going wider than f/1.8, your target should be f/1.4 lenses.
Third, because the 77D's sensor is physically larger (22.3 mm x 14.9mm) than the G7's (17.3mm vs 13mm), at the same exposure, shutter speed, and video resolution, you should expect the 77D to produce cleaner output (less noise) in low light. Basically, at 1920x1080 resolution, the virtual pixels on the 77D are larger, so have more light to work with than the virtual pixels on the G7. So even when both cameras have the same exposure (same amount of light per square mm of sensor), the 77D's pixels are getting more light per pixel, and it should generate the cleaner image.
If you're serious about this, you should conduct your own tests with both cameras side-by-side in low light at the same exposure settings (doesn't have to be f/1.7 for the comparison, just make sure the ISO, shutter speed, and apertures for the two are the same). Then compare the image quality. If I'm right and the 77D's output is cleaner, crank down its exposure (keep the shutter speed the same, stop down the lens to a higher f-ratio, increase ISO to maintain image brightness). When you judge low light video quality to be the same on both cameras, compare the two f-ratios. That'll give you an equivalent f-ratio for the two cameras (for producing same-quality low-light video). e.g. If the 77D's video at f/3.5 matches the G7's video at f/2.8, then f/1.7 on the G7 is equivalent to (1.7)*(3.5)/(2.8) = f/2.1 on the 77D.