No it doesn’t matter which DH you use, they are only interpreters and don’t impact things like battery (some can improve battery life by reducing the amount of polling the platform does it can’t make it worse). It could be due to some apps continuously communicating with the locks (check your device event logs) or the locks being too far from the with with no repeaters in the z-wave mesh. Ideally the lock should be no more than 15-20ft from the z-wave repeater to reliable and efficient operations.
The other reason why the status isn’t updating is that the lock is too far from the hub for a reliable z-wave mesh communication, same as the last point above. Try to add a z-wave repeater between the lock and the hub. Then reboot the hub and do a z-wave repair.