You may very well be at the limits of your equipment. The best you can do is to set the aperature to f/4. Don't close down at all. Then, per how you want to freeze or show motion, set your shutter speed. The last variable is then ISO. So the faster you'll be setting your shutter speed, the higher your ISO will need to go.
Moving forward, this is where a newer camera would be a huge benefit. Especially if going full-frame. However, on the latter point, do examine your images to see how often you're using focal lengths of 100mm, around 200mm and around 400mm. If you find you're mostly at 100 to 200, then you can use the lens on a full-frame camera with longer focal lengths to compensate for the wider field-of-views you'd be getting. But if you're mostly taking photos in the 300 to 400mm range, moving to full-frame may not be ideal (you'd need to crop photos to get the more narrow field-of-views; losing resolution).
A newer camera body will give you much better ISO performance. The exposures would still be the same (i.e. you'll still be finding the need to be at ISO 1600 or higher). However, the amount of noise in an ISO 3200 image will be much lower than the amount of noise in your T7 at ISO 3200. Could be around 3 stops worth (i.e. an ISO 3200 image on the new camera could be as if you took it at ISO 400 with the T7).
Beyond a camera body, would be a new lens. But price here will dramatically accelerate especially if wanting faster than f/4 for long focal lengths. e.g. an RF 400mm f/2.8L IS lens is around $12,000
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Ricky
Camera: EOS 5D IV, EF 50mm f/1.2L, EF 135mm f/2L
Lighting: Profoto Lights & Modifiers
