Surprisingly, there's still another interpretation:
Root ING- + abstract suffix _we_ + root IS-, "first/foremost
I'm aware I have to supply quite some evidence for my strange
1. _Inwe_ is a variant of the name _Ingwe_, the first high-king of
the Eldalie (LR, Index "Inwe" and "Ingwe"). There is at least one
other similar derivation, _Inwir_, the house of Ingwe in Lost Tales.
2. The root IS- showed up as _ist-_ in all known derivations (Etym,
I see one problem: the glosses "knowledge" and "(mind-)mood" seem to
be incompatible. But that may be just us: "knowledge" needs not to be
restricted to rationality in other cultures, or in Tolkien's
understanding, and the fact that he used the same element _ist_
for "feeling, sensation" in Gnomish (cf. Beregond's message 105)
could be a third evidence in favor of my hypothesis.