The most viable long term solution for long-haul air transport will probably be carbon-neutral liquid fuels. For example, in principle it could eventually become possible to genetically engineer algae which pulls CO2 out of the air and produces kerosene.
Eventually? In principle? Ethanol is a thing, just not one that was able to compete without taxing its competitors' externalities. Not sure how the math works out for jet engines, but I suspect it works out better than batteries.
Maybe it's better than petroleum? The hell? It's not only better, EtOH becomes entirely neutral in the limit where it takes over. The carbon released from burning all comes from the plant, which in turn all comes from the air. All other carbon costs are incidental (e.g. it doesn't make sense to immediately convert transportation, farming, and production equipment) or one-off and amortizable (ploughing fields).
For long haul air transport we would have to redesign engines, fuel systems, and airport infrastructure to use ethanol safely. And even then it would make flying less efficient because ethanol contains less energy. Synthetic kerosene or something similar would be an easier transition and give better results.
