> . . . it looks like I can't get the key out
> without breaking something. Do you think I should try it anyway?
Here's a rough sketch of my method for pulling a keycap from the lower tier. The spacebar serves as a fulcrum. The "trick" is to pull the key fairly straight up; that's why I use both hands, my left hand serving to counter the torque being applied by the screwdriver in my right hand. Helps to have strong fingernails.
Every keyboard I've attempted to disassemble has been designed to come apart like this, without breaking. Work slowly, gently, but firmly. Heck, you can't make it much worse-- and the keyboard has to be either fixed or replaced. Good luck; take your time.