You need three things to start an engine: Air, Fuel, and Spark. It turns out that a coil coming unpinned may result in a lack of spark. Who knew?! These coils are 034's IGN1A coils that they supply specifically for C4 cars. The quality, unfortunately, was lacking in this instance.
I ended up completely depinning several of these connectors and purchasing new ones, then crimping new terminals on and re-pinning them. I did quite a thorough "pull test" after to verify everything is seated fine now. I have to assume they just had an apprentice that got lazy at some point. At any rate, they should be fine now.
During this time I also tested the Cam Position Sensor and replaced the Crank Position and RPM Speed Sensors. I also purchased a tester from Marc @ Efi Express so that I could test and verify it is working. I even switched out the CPS sensor on the bracket he provided with a new one, riveted it in, and then cold welded it.
CPS tester showed that it was working just fine on crank. Yay!