I would say the sense of this 分 usage is to indicate a kind of "proportional increase" - the 分 indicates that whatever comes after it is increasing in proportion to what comes before it.
In the first sentence, Momo may or may not be a particularly つかみ所のないやつ aside from this, but the fact that s/he is always smiling adds a certain amount of つかみ所のなさ. The 分 represents this "amount" that is added.
Similarly in the second sentence, the need for 技術 increases in proportion to the lack of 基本. (If you consider the amount of effort put into something as a constant, then not having to devote as much effort to mastering the basics means you have to devote that same effort to mastering advanced techniques instead, so the "proportion" element is fairly literal in this case.)
The third sentence is the same sort of idea - the apprehension he feels about going to the conbini now feels more immediate (more リアル) in proportion to how casually he usually goes there.
You might be able to find more information on this usage by looking up その分, which is a very common form it appears in.
I'd say this usage is related to the "hypothetical partial involvement" usage you referred to, because they're both narrowing things down to examine the effect of a single factor. When you say 見ている分にはいい, you're saying "I don't know about other aspects of it, but to look at it's fine" - talking about just the appearance to the exclusion of other factors. And when you say 毎日見ている分、なじみがある you're saying "I'm used to it, particularly because of the part where I see it every day."
The main difference between the two, I suppose, is that ～分には tends to imply that this focus aspect contrasts with other aspects of the same thing (eg. if you say "it looks fine..." you're implying that other aspects of it probably aren't fine) whereas the ～分 usage tends to imply that this aspect complements other aspects (ie. you're looking at one factor contributing to a larger effect.) Though ～分 may imply a contrast with other things that don't have this factor (eg. the 基本が少ない分、技術が必要 sentence implies that breaststroke is more technique-focused than other swimming styles that have more basics to learn).