Basically you need another way to talk to the Android tablet, right ?
Here some basic ideas:
1) Add wifi to your arduino, there are plent of ways to do that
Longest range and likely most expensive
2) Add bluethooth and connect via bluetooth
Range more limited and closer to hardware
3) Add a NFC shield and communicate throu8gh P2P NFC
Very close range, maybe the available bandwidth is a problem for you
4) A bit dirty .. You can hack the Nexus 7 to provide USB OTG if I recall right.
You would use a FTDI like USB to USART device and directly plug your board into the USB slot of your nexus.
This likely involves changing the kernel, I remember there was also something about a modified USB cable to add power to it and you would need to change your nexus7 into root mode (it's easy but involves a data blackout). Quite some effort.
5) Another funny method, you can use the display, front camera and LEDs/photodiodes to make a light based communication.
This is even more limited than NFC in range.
I have seen that method being used by banks to communicate from online banking to a crypto-device.
6) As a finishing idea. you said you have an ADK cape and you can not use it due to pin constraints. You can consider to add a second AVR/arduino to your project which just acts as relay between android and your main AVR.
You can use highspeed (400k) I2C or SPI between the AVRs, so you can go up to some megabits if you need the bandwidth.
If I recall right such an approach is used for the large Arduino Mega2560, it has a small AVR aditionally on board which acts as USB relay instead of the usual FTDI method.
There are many ways to communicate with the android tablet, quite a few of them are useable in my opinion.
As soon as you are able to communicate all you need to do is write a simple protocol and the show can start.