If you have more than one output active at the same time, you must derate the current. According to ULN2003 datasheet (SOIC package, which is what you want to use I presume), if you have 4 active outputs with 50% duty cycle, the maximum current per transistor is only 200mA.

ULN2003 is not really a "motor driver" anywhere outside Arduino world. I would look into something like MOSFET arrays or even discrete MOSFETs instead.

Now, if you want to try something interesting, there is Texas Instruments DRV8860. It's an 8-output driver with a shift register and serial input, so you can save a lot of I/O pins.