Just now saw this. In case you have not identified this, those seed pods definitely look like ash to me. Box elder seeds look just like maple (because it technically is one) with 2 seeds and 2 wings attached to each other while ash seeds are single seeds with a single wing.
Edit to add: Hackberry by the way has little berries without wings. They can make a horrible mess if growing over a side walk or when the birds eat them and later deposit them on your car.
--Nathan, TX. Hire the lazy man. He may not do as much work but that's because he will find a better way.