How this currently works is that when we notice a substantive overlooked story, we add it to a pool. Every now and then software picks one from the pool and randomly places it near the bottom of the front page. It does that by reducing the time decay and/or adding a small number of points. If too much time has gone by for a small change to suffice, the software doesn't try, and instead we sometimes email an invitation to repost the story.
This system would never add 15 points, nor place a story as high as the middle of the front page, so if that's what you saw it means the community noticed the post at the bottom and took it from there—which is the intent of doing this in the first place. We don't much care which stories get taken up this way vs. which don't. The idea is to do the minimum necessary to give high-quality stories a second chance and mollify the cruelty of /newest.