This might not be the answer you're looking for, but I don't have a better way for downloading DB from phone. What I will suggest is make sure you're using this mini-DDMS. It will be super hidden though if you don't click the very small camoflage box at the very bottom left of program. (tried to hover over it otherwise you might miss it.)
Also the drop down that says no filters (top right). It literally has a ton of different ways you can monitor different process/apps by PPID, name, and a lot more. I've always used this to monitor phone, but keep in mind I'm not doing the type of dev work that needs to be 120% positive the database isn't doing something out of the ordinary.
Hope it helps