Okay, already some good input - and thank goodness I've got most of this covered. For cicerone imposter, the good news is that, as an outdoor receptacle, I know factually that this outlet is already on a GFCI. And in the floodlight interim installation, I religiously maintained the ground wire throughout the circuit.
For fishin, I did confirm that there was a sufficient amount of capacity on the circuit/breaker. As you probably already noted in the graphic, this installation is using the appropriate size ROMEX wiring. I will concede again, that admittedly the use of the outdoor three-wire power cord splice (which you correctly spotted) was not the optimal installation, but it was a stopgap for a couple of days to ward off the "burglars". And again, the splice connection was sealed and secured six ways to Sunday - since I acknowledge that it was the weakest link in the whole circuit.
I did study the idea of fishing the installation into the exterior box from below, but give the thickness of the deck and height position of the exterior box, the whole thing (below the level of the deck) is effectively sitting on top of the sill, which is also sitting right on top of the concrete foundation - so absent a jackhammer and the consulting services of a structural engineer, coming in from "below" was not in any way a viable option. So, in the brighter light of more information, which I probably should have provided upfront, any suggestions for the front door approach? I've seen what appear to be outlet adapters, which allow mixed (plugged outlet + wire) installations in this type of all-weather box. I hesitated to suggest a response, so as not to predispose anyone to a solution, but that's looks viable to me. I was hoping that someone would independently confirm that approach, and still will - even though I've maybe predisposed folks to an answer now.
And am I mistaken, or has the format of this forum changed recently? I could hardly find the core forum topical areas in order to post this? Maybe it has changed, but I just haven't picked up on the "intuitiveness" of the new look.