I was able to figure this one out shortly after posting.
The issue was, in my shortcode that I wrote, I was echo-ing my variable.
I changed that to return instead of echo and now things are rendering in place as they should.
@cunnie – you’re right. I disabled that plug-in and all is good now. I don’t really need it, so I’ve gone ahead and deleted it.
@wpmudevsupport11 – I’ve gone ahead and removed WP All Import. I am not sure what exactly was causing the issue, but I’m thinking something got picked up in the cache and WP All Import was assuming that post ID should be there, but failed when it couldn’t actually find it.
Thanks for your support, guys!