Moving them may cause them to stop laying - they don't seem to cope well with change, so I'd find somewhere they can permanently be. I'd put a solid base on your cage at least, and if it's on the ground I'd put a board around the bottom at least 20cm wide so that no rats can try and grab them at night.
You can pack them in like sardines, but it's not ideal. Minimum recommendation is 0.5sq/ft per bird, but that's pretty crowded. 1 sq/ft is more commonly suggested which is about 0.1sq/m. They do enjoy a bit of space to leap around and play.