I have seen this chain plate design in the accessory after market. I don't understand why they would not have made the join in the vertical side of the links, as illustrated in your plan. It would be much easier to work with and have a higher tensile strength as well, making it harder to pull apart under stress/load.
With that said, I have had success cleaning the joining ends. I had to attempt to file the ends flat to achieve a better surface to solder. I used silver solder paste, which contains its own flux. This made it easier for me. I over applied the solder and then hit it with a small open flame torch, with decent results. But honestly, I would NEVER do it again. As someone else mentioned, in the future I will just create my own. It would be about the same amount of work. I would not be cursing anyone. And, I would have a greater, proud feeling of accomplishment.
If I had the pieces you have, I would keep the deadeye strop and plate, discard the chain links. Pick up some hardened brass wire of the correct diameter and scratch make the links with the joins on the sides. Make sure you buy "hardened" brass wire, it makes a difference. You can make a simple jig from a block of wood with two nails or drill bits distanced to equal the length of your desired chain link. Then wrap your wire, cut, solder and blacken, rinse and repeat. I used to have photos of how I did this, but think I lost them when I upgraded my phone.
Best of luck!!
PS, Actually, I just saw in your link the process I was describing. This worked well for me. Wish now I had read the post before I typed my version of War and Peace!