I must apologize as I phrased it poorly, about having gotten the idea from Self Insert. I should have said it was similar to an idea used by them. Of course with a name LIKE Self-Insert you expect such things to begin with. I didnt mean to offend, I just phrased it poorly.
In regards to creating an idea, here is one that happened to me. Rather amusing at that. I write fanfics at times. Well, I came up with an idea and began writing it, only to find out another author(a good friend of mine) was working on a story that was almost identical. The core idea was the same, how we were implementing it was drastically different. It was scary how similar the core idea was though, just the method of causing the change differed a bit. The focus of the story differed, but the backdrop was almost identical, the fact that we both had similar goals in the story was even scarier yet.
So, I do understand, I've had ideas galore for a fanfic, only to find out its already been done to death. Its hard to be original, the best you can do most of the time is take a used idea and put your own personal spin on it.
Self-Insert has them dealing with the core characters in order to achieve their goal. You have them not even associating with the characters, just in the same area as them. Your goal is more personal(find the missing friend), while theirs is a touch more abstract in ways(find a way home).
Anyway, apologies for implying you took the idea from them. This is as you said, sadly a very common occurence. I had that happen to me as well with the story I mentioned. Someone thought I was continuing the work that he'd started. I confirmed that it wasnt.
Anyway, keep up the good work.