Alright, I see what you mean. Thanks for that clarification!
...I should clarify that I am putting this script on a separate object that is a moving platform, separate from the player, and part of the level. This platform should be pausing whenever the pause event is started, and it does, as it's 'pause mode' property in the inspector is set to inherit. The problem is, however, that when the player jumps on the platform when the platform is in the pause state (and the player's 'pause mode' property is set at process), the player will slide in the direction that the platform would be going if the game wasn't paused (even though the platform itself isn't). Could this be a problem in the player's script instead?
Here's a link to each one of the scripts that may be contributing to the problem:
Player Script:
Moving Platform Script:
Pause Menu Script: 
Thanks so much for your help, and for how quickly you answered. I really appreciate it!