Why are you opposed to have an "unfinished" edge exposed? It is just color variation? Once you cut the edge that will be exposed, can you dye it to a color similar to the rest of the plank so it doesn't stand out as much?
The other thought that crosses my mind is to cut a small piece of transition with a 45 degree angle on both sides so that it essentially forms a triangle so it butts up against the cap piece and the end of your flooring run. Then you have no exposed edges and it fits the area you already have. Because it won't lock together, it would have to be glued to the end of your transition piece so that it stays put when fastened down.
An unfinished/exposed transition piece end will stand out (like you mentioned due to color) but i would also think it would be a tripping/toe stubbing hazard. Sure, it's really close to the bannister, so i'm not sure how many feet will be traveling there, but i would still be worried about hitting it with a vacuum, etc.
I've scratched my head a bit on your 2 45 angles, and i'm not sure i understand properly. The only way i see that working is if the triangle has it's pointy edge extending towards the laminate flooring, and that seems dangerous too. Is that what you meant, or something different?