No, it's not mostly overkill, it's 90% overkill. Modular is cool because when two pieces doesn't work you disconnect them and find out why they work independently but not together. That modularity works for both mechanical and logical systems But you don't have any 'interconnected' items - it's all linear.
I don't think you realise how spectacularly -annoying- simply -maintaining- the levels of 'disconnectedness' you have designed will become. 4 Arduinos require 4 totally different sketches. Each sketch will require more volume of code just to talk to the master Arduino than is consumed by the individual item it's controlling.
You're also up to 5 motor shields. DC control is about the simplest control, and the most vastly produced addon so there are tons of options.
At ebay look up 8 channel relay board. But that's only for unidrectional board, and no speed control.
If you need speed control you need a FET board.
If you need to reverse a motor you need an H-bridge board, which generally includes speed control.
The RGB LEDs are a very common separate board also.
Yes, the wifi and MP3 are shields.
We're up to SEVEN SHIELDS. Now think about disconnecting the 4th shield from the stack, unplugging the top 3, pulling off the 4th, plugging the top 3 back on, doing whatever, and reversing the process to restack them. Sometimes modular isn't convenient, to the point of extremely annoying.
It won't work 'stock' anyway because there are a limited number of address pins to the motor shields. You'll need to bend wires out and flywire them down to other address pins. Now you can't even 'simply' unplug a shield from the stack without also unplugging/replugging the flywires. (There may be incompatibility between the couple of required shields anyway. Not likely, but don't -deliberately-make things any more complicated than is unavoidably necessary.)
This whole stacked thing also DRASTICALLY multiplies the power consumption!!! It'll need enough batteries that are half of the box's weight!
I -was- gonna say yes you can add a switch panel that powers each of these separate boards to make you feel better about everything I talked you out of, but it's unnecessary and you will never use them. Again, there is no mechanical interconnectedness. To disable an item you do that in software. But again this system is so 'linearly-simple' that there won't -be- much debugging. Start with the first required items - display and 'on' switch. Then work on further mechanical items one at a time. Along the way, you won't be doing any disconnecting/disabling of any of the previous items, and by the time you get to the last item it's finished.
All of the above can be controlled by a Mega. (Possibly an Uno but I haven't counted up the IO pins.)
Modular is good. But that doesn't mean writing the letters m o d u l a r on separate pieces of paper, because it makes it much more difficult to read. I understand you want to break the project into different sections, and you -did- that part right, but you have gone as far as printing the letters on separate pieces of paper, and mailing them to 7 different states. 
Gotta reign it in or it'll become extremely unwieldly.