I recently got some rather bad news in my life, and that's weighing me down. I may be once again slow to respond, and will likely need to take a bit of time to sort some things out. DMing, as much as this is a module, is taking a toll greater than your usual RP does. So if I'm not responding as quickly as you may have come to expect, or pass the time limitations that we have all agreed upon on, I can only ask you to forgive the transgression.
Anyhow, now that I am here, I'll point out that the cage door does indeed have a keyhole
@Ryonara. It's one of those old fashioned heavy open from both ends types, and rather large at that. Stuffing it may not be impossible, but it'll take a bit of time and opening it again takes more force and less fine manipulation as you might desire. If you commit to the task, you will get it mostly done by the time the next event takes place. This acceptable?