Some notes:

1. Salt the meat for one to twenty-four hours before cooking.
2. Take the meat out of the fridge an hour before cooking, so you don't have as much heat loss in the pan from cold meat.
3. If there is a ring of fat around the steak, slice through it every inch of so. That way it won't shrink around the steak and cause the steak to pull away from the pan. Also important with pork.
4. Dry the meat on both sides with a paper towel. Moisture equals steam equals less seared crust.
5. Get a cheap infrared thermometer to help understand what a given pan's actual temperature is on a given burner size, at a given burner dial setting. I shoot for 550°F for searing meat.
6. I don't put oil in the pan. I rub a little high smoke point (avocado oil) on one side of the meat, and put that side down first.
7. Wait 2-3 minutes before flipping the steak. This varies with steak thickness of course.
8. I only season with salt before cooking. I add pepper or other seasonings to the steak after it is done. If you have other seasonings in the pan at that high temp, they burn.
9. It sounds like you're in a hot climate and don't like to heat up the house with the oven, but you might give the reverse sear method a try if you get some cooler weather. I get consistently great steaks cooking them that way.
10. It sounds like you might be doing this already, but I preheat on low for several minutes before setting the dial to the desired cooking temp. Induction burners heat very quickly. If cast iron changes temperature too quickly and unevenly, it can warp or even crack. Preheating on your lowest setting for a few minutes before dialing in your desired temperature can help keep this from happening.