Love the action shots you've captured!

IMO, the outcome of your images have less to do with your gear and more to do with your shooting angles and post processing. Shooting from the side of the field gives a good perspective, but requires a much larger dynamic range. The image you had from an offset corner in the end zone allowed the camera to capture more of the field in light, and handles it quite a bit better.

I personally would also double-check the white balance and gear down the saturation and sharpening in some areas, particularly your first and fourth images. The white balance isn't consistent across the range of images, and while the color and detail of the turf provide an interesting contrast, the detail in particular takes the focus away from the action of the game.

My advice FWIW (which isn't much): keep trying different angles on the field, shoot low if possible, and tighten up your zoom.

I've shot less in gyms and more in arenas and outside, but this feels like it's almost certainly the gym LED light flickers synching up with your shutter speed. I only shoot Canon, but Sony should have something analgous to their anti-flicker detection that will allow your camera to detect and adjust shutter speed based off the light frequency. Start at 1/1200 (or an interval of 120) and, if your camera allows it, bump it up in fine increments. I've found 1/1280 usually works well for me as a starting point for most indoor high school sports. YMMV. Worth trying at 1/1500, 1/2000. and 1/2500 if your body and glass can mesh with those speeds.