Yeah, we realized that recently 
We are going to try to do just 6 of them now.
On a good note, we found a bunch of IRL540NPBF that CrossRoads mentioned in our school lab. We are having issues getting it to work.
We connected our solenoid to the Drain, with a diode in parallel to the solenoid, and we connected the other end of the solenoid/diode to VCC (another power supply separate from the Arduino). We connected the Source to the ground and the Gate to the logic output of the shift register. However, it seems that the Drain reflects what the power supply gives off without reacting to the Logic input at the gate. How can I make it so that the NMOS cuts off any current going into the Drain when there is a logic "0" from the shift register.
A quick note: Our shift register gives off approximately 4 volts, and 20mA when "on".
If a picture would help visualize this better, please let me know.