A big disconnect between TOS designs and designs from TMP onward is the level of surface detailing. It got ramped up big time and increasingly so as time went on. It started to reflect the somewhat industrial look of Star Wars that became the new norm for sci-fi hardware that now had to reflect a more accessible near future sensibility. Gone was the look of a future that reflected a science and technology that could be barely understood by our contemporary knowledge.
I actually like the OP’s design better than the TSFS BoP.
Now that I can see the video I see where you are coming from. I do agree with the poster that said that the ship was probably facing the other direction from what this designer came up with. As far as the video's "scout ship" discussion I think this is not something that needs to been seen as a contradiction. A vessel the size of USS Grissom with lots of guns would be a "scout ship" and yet also a "warship" to me. If it's acting like it is going to fight, shy not call it a "warship"?
Also, I don't think there were two ships. One used the distress signals to call them away, then circled back. Sulu recognized that a Klingon Bird-of-Prey could cloak in Star Trek III as though he'd seen it before. Even D7's masquerade as sensor malfunctions, even when not crewed by Romulans. Even without a true cloak, I imagine such a ship could have circled around without being clearly seen.
Maybe that glow was a shield designed to hide the ship's exact position and configuration without fully obscuring it?
The video shows 11/20/67 for the D7 design date I believe. Memory Alpha reports filming done in May 1967, and music in July of 1967, and airdate of 12/1/1967. With that timeline, it seems to me that the episode could have been almost complete, minus the Klingon ship, and Jefferies could have designed the D7 in response to the episode, but there bee no way to actually include it, and that could be why we don't see it until the next season. However, with the script mentioning a scout vessel, I'd rather think that, even in the mind of the designer the ship seen in this episode is not a D7: it is a different class, unlike what TOS-R showed.