This fall my school ordered 24 Super Kits. I had to figure out how to organize them so students could begin to build their clawbots.
Link to my solutions
Some surprising ideas there. Hot glueing parts to bins is of course a practical way of showing where each part goes, but somehow it makes me feel uneasy 
Why did you decide against using the bins provided by VEX IQ?
Do you really need pliers to disassemble parts?
I really like the way your students decorated some of their robots!
The plastic bin and one tray that comes with the VEX IQ super kit will not hold all of the pieces unless one just dumps them randomly into the bottom of the plastic bin. I want the parts to be kept separately so students can quickly find what they are looking for. Gluing on a real VEX piece rather than a photo is fast and easy: student have no excuse for not knowing where a part goes.
The short blue connectors can be hard to pull off. I have a tool box full of pliers so that is what we use.
I put 2 trays in each of my VEXIQ boxes so you end up with 3 layers altogether - motors and larger parts in the bottom of the box then 2 layers of other parts. You still have 2 or sometimes 3 different parts in each section but that is not too bad. I try to make sure the parts sharing a section are different colours.
I often push small pins out with a bigger one if you can get to the other side. It is hard to stop pupils using their teeth so I understand why you have pliers.