Gdtyjr

Continuing How to get glossary terms to properly typeset subscripts/superscripts?, let's consider the following input:

documentclassbook
usepackagefontspec
usepackage[ngerman]babel
usepackagemathtoolsmathtoolssetmathic=true %%% See http://tex.stackexchange.com/a/3496/
usepackageamssymb
usepackageunicode-math
setmainfont[Ligatures=TeX]TeX Gyre Termes
setsansfontTeX Gyre Heros[Scale=0.88]
setmonofontTeX Gyre Cursor
setmathfont[Ligatures=TeX]TeX Gyre Termes Math
setmathfont[Ligatures=TeX,range=setminus]Asana Math
setmathfont[Ligatures=TeX,Extension=.otf,range="2A3E,BoldFont=XITSMath-Bold]XITSMath-Regular%%% The fat semicolon
usepackage[unicode,hidelinks]hyperref
usepackage[makeindex,toc,nogroupskip,nomain]glossaries-extra %%% glossaries-extra internally loads glossaries, and glossaries according to its documentation should be loaded after hyperref.
%%% The next hack improves how hyperref jives with svindd.ist, see https://tex.stackexchange.com/a/429446
makeatletter
def@commahyperpage#1@@commahyperpage#1,,,\
def@@commahyperpage#1,,#2,#3\%
 ifx\#2\%
 HyInd@pagelink#1%
 else
 HyInd@pagelink#1,,HyInd@pagelink#2%
 fi

makeatother
setglossarystylelong3colrenewcommandglspagelistwidth10em
GlsSetQuote+ %%% Hack to work with makeindex
usepackage[babel=true,verbose=errors]microtype
newcommandNNZglsnot:nonnegativeNat% ℕ_
newcommandNNPglsnot:positiveNat
newcommandfiniteWordsSet[1]#1^glsnot:finiteWordsSymbol %%% Sequences
newglossary[nlg]notationnotntnSymbolverzeichnis
makeglossaries
newglossaryentrynot:positiveNattype=notation, name=(ℕ_mkern-2mu>0), text=ℕ_mkern-1mu>0, sort=Nplus, description=Die Menge positiver ganzer Zahlen.
newglossaryentrynot:nonnegativeNattype=notation, name=(ℕ_mkern-2muge 0), text=ℕ_mkern-1muge 0, sort=N0, description=Die Menge nichtnegativer ganzer Zahlen.
newglossaryentrynot:finiteWordsSymboltype=notation, name=(cdot^*), text=*, sort=*finiteWordsSymbol, description=Gegeben eine beliebige Menge (Z), bezeichnen wir mit (Z^*) die Menge aller endlichen Wörter (also, endlichen Sequenzen) über (Z).
begindocument
What we typeset is:
[finiteWordsSetNNZ finiteWordsSetNNP]
(finiteWordsSetNNZ finiteWordsSetNNP)

bigskip

However, the visual appearence leaves much to be desired. The star should better be closer to the double-struck capital N and a little bit higher, such as in
[ℕ^raisebox.1ex$scriptstyle *$_mkern-2mu>0 ℕ_mkern-2muge 0^raisebox.1ex$scriptstyle *$]
(ℕ_mkern-2mu>0^raisebox.1ex$scriptstyle *$ ℕ_mkern-2muge 0^raisebox.1ex$scriptstyle *$)\
and all the symbols should be still properly linked to the glossary.
printglossary
enddocument

Compiling with xelatex file && makeindex -g -s file.ist -t file.nlg -o file.not file.ntn && xelatex file gives us this:

How to adapt the code in such a way that the macro calls finiteWordsSetNNZ and finiteWordsSetNNP produce a visually pleasant output without losing the links to the glossary and perform as before for the other actual arguments? If that's too difficult, I'd even appreciate single macros finiteWordsOverNaturalsZ and finiteWordsOverNaturalsP that would produce the visually pleasant representation of the notation for sequences of naturals with/without zero?