From reading your list, which was and is an extremely useful resource, that I was very glad to find
I came to the conclusion that as far as I had the mental powers to work out, the uses were consistent with pu.
For instance; ike la -- this is just setting up the context of "bad", so the statement that follows it, is a statement that is in that context; ie unfortunate.
I remember you use ante la for otherwise ? again the context is setup that the statement that follows is "different, altered, changed, other", in the context of "other" - this.
Another was sama la - you use/report that is similarly ... again context of what is the "the same" - this... etc...
Follower of the official dialect of toki pona as presented in the official book; Toki Pona, The Language of Good by Sonja Lang.