Okay, got back with my colleague and received another WP7611 module. This one worked!
However, I also realized while replacing the CF3 module that there is another metal lid that can be affixed over the module that is meant for lower-profile modules (like the WP7611), whichI used that lid. Which after realizing this, I tried out the other loose WP7611 I was testing previously, and it also worked. So I believe the issue I was experiencing was due to using the wrong module cover on the MangOH Red.
As for our two custom PCBs. My colleague informed me that someone had re-flowed these WP7611’s in-place of a WP7603 that was previously on the PCBs. So it appears these two devices are faulty due to a bad re-work.
So I guess overall, this was simply a case of human error all around. 
Thank you again Jyijyi for all of your help!