I have not used any modern inkbirds - the early ones were so terrible that I just stuck with Rancos that never let me down. Maybe a new inkbird is better, but I don't know. You could use a Ranco like this... set it high and have it on a timer with the lights. I don't really see a downside. This will be lots of wattage and on all of the time, so would go industrial over hobby grade for this.
When my tanks get hot from Halides, they take an hour or two to cool back down, which is a good thing for me in such a dry climate where heating costs so much. I would not worry about a short cycle too much. Besides, the ballasts won't allow too short of a cycle.
In all honesty, if your AC goes out, you are going to have a few more days than just that first one. If this happens, fan over the tank that comes on when the halides come on was able to get me by in Missouri with the 100 degree days and 100% humdity. Don't get cute and wait until the tank starts to warm up since you will already be behind. Some would change their light schedule to run more into the night in the summer like 6:00 to 2 AM the next day when it was cooler - the tank did not mind.