I've been carrying a set of 920 Chipcos + 80ish old-school ceramics from my car, upstairs into my local club, and back to my car once a week since the spring. My birdcage only has two screws on the bottom, and I'm using standard racks, i.e., 20-chip barrels of Chipcos sit one chip loose and shake around a whole lot.
I've never had a concern. It feels quite sturdy despite the chips shifting around. I haven't noticed any looseness or other issues in the case itself.
That said, I don't really need 1,000 chips for the game and will probably pick up a 600-chip carrier and some Chipco racks, eventually. But no actual problems with the birdcage.