I feel your pain.
I work for a law firm one day a week, that has a conveyancing department and I still had to chase continuously. In my case they were just snowed under with work… but chasing and ensuring that you aren’t just going to sit quietly while they prioritise their workload is likely going to be more fruitful. I’d just keep them reminded, a lot - provided you’re on a fixed price conveyance and not paying by the hour.