I'll get straight to the point: they don't exist.
The lack of consistency annoys me, as I'm sure it does others, too. It's part of what makes me in favour of the connective reform involving such things as {gije} as a replacement for {gi'e}, which would equally provide us with a means for producing non-logical bridi-tail afterthought connectives.
.i mi'e la tsani mu'o
P.S. It occurred to me that they didn't exist when I tried translating "We do what we must because we can" as *{.i zukte lo semu'igi se bilga gi se zifre}, but {TAGgi} only works for non-tanru-internal forethought connectives. Using {zukte semu'igi lo se bilga gi lo se zifre} is out of the question because the meaning is different. I want to get at the meaning of "we do the (things that we must do because we can do them)" rather than "(we do the things that we must do) (because we can do them)." Of course I can resort to a zo'e-noi construct as a patch, but that's far more inelegant: {.i zukte zo'e noi ke'a semu'igi se bilga gi se zifre}. In sum, the fact that these types of connectives don't exist is frustrating and inconsistent and should be fixed in order for the language to be in accordance with its philosophy.