I wanted to update on what I found just so nobody is wasting any more time on this. After more digging, I found that multiple outputs were in the system ladder and the user ladder that would cause the servo off signal 1 and 2 to come on. These were outputs that are normally open for use in our standard robot setup at my company. All the robots on this build are repurposed, so I can't say for sure why these outputs were controlling the servos. Regardless, I have updated the user ladder and used different outputs instead of the ones used as contacts in the system ladder. I think the reason it was apparently stopping on the wait statements is simply because the robot program would go over the output command fast enough.
I've only fixed the problem in the dx200 that was causing me the most trouble, but I'm assuming the NX100s have a similar problem with their setups. I will update when I am able to look into those in case I'm still having issues.