I had reached out to our hosting support at WP Engine, and they had assured me it was nothing on their end! Doing further testing, I cloned the site over to one of my siteground accounts and figured that it WAS an issue with one of WP Engine’s plugins within the wp-content/mu-plugins folder and that every time I deleted it, there was a script that would re-add the plugins.
Very frustrated with them, but am definitely relieved.
Thanks for your help!