ok so I got home from work and I just soldered on two 0.1uF capacitors on my L293 IC and one on my logic gate IC. I reran my test and there is still a slight jerkiness to my servo when the DC motors are engaged but it's not pulling hard left like it was 
My coworker also gave me a 470uF/1000uF capacitor to put on my two voltage supplies, so I'll be curious to see if that totally clears things up.