Motor Shield Runs Better on AC than DC

I've never touched the jumper - it's always been on the motor shield.

That's what I meant.

If you want to run without the USB connection you need to also plug ext pwr into arduino ext dc pwr jack. Without the jumper and without ext dc power into arduino, you need the USB to provide 5V.

The little jumper on the motor shield connects the USB +5V to the Motor shield +5V. If you don't have the USB connected the L293 has only one other source for that +5V and that is the arduino onboard regulator (which is a different +5V source than the USB) which receives power from the arduino ext. dc power jack.
Option A: USB plugged in and jumper installed.
Option B USB DISCONNECTED, jumper installed, Motor ext. pwr connected (greater than 7Vdc)
Option C USB DISCONNECTED, jumper installed, arduino ext. dc power jack supplied by 9V dc.
Option D USB DISCONNECTED, jumper NOT installed,Motor ext. pwr connected (greater than 7Vdc) AND arduino ext. dc power jack supplied by 9V dc.

If you remove the jumper and only supply pwr to the motor shield ext pwr terminals, you will see there is no voltage on the Arduino Vin, hence no +5V to either the arduino or the L293 VCC1 (pin-16). The jumper connects the ext motor pwr terminals to the arduino Vin allowing you to run everything off that power , if and only if it is high enough voltage to supply the arduino +5V and the L298 +5V. If the jumper is removed and you supply motor power and then supply power to the arduino ext dc power jack , you will see that the ext dc power jack supplies the arduino Vin and hence the L298 VCC1.
Those are your options.
Hope that's not too hard to follow.

The problem occurs when I put the motors into the chassis. That's it. It's like putting them in there makes everything begin to malfunction off of the same DC power that I used when they were outside of it, but when I use USB, it all works fine.

However, when I place the motors in the chassis, and then connect the battery (7.5V, 5x 1.5AA or even 9V, using 6x 1.5AA or a 9V battery), not all of the motors run. Some stutter, some spin for less than the req. time, but regardless, it is not fluid. Seems to short circuit itself.

You need to clarify this statement . How many dc power sources do you have plugged in when it is in the chassis and where ?