6/9: Third inversion of 7sus4
11th: Sometimes the second inversion of 7sus4
11no3no5: Second inversion of sus4
13th: First inversion of add9 (although (add4)c is available it no longer functions)
7th with sharp extensions: Use #5 directly
7th with flat extensions: 7, except M7b5, respelled as M7#11 using viio24sus4
dim7: sometimes an appropriate inversion of the dim chord from any mode borrowed in the relative Major
augmented: also use #5 directly, but while respecting voice-leading, never use the second inversion
An example of C13 - A6/9 - FM7#11 - F/G.
#9: M if the minor third appears in the melody, m if the major third appears or neither appears
11no3: 7sus4
Bdim7/C etc.: iiΓΈ24
Since Hookpad 1.2.0 it is possible to clone any Theorytab containing them, and then copy and paste the inverted suspended chords or #5 chords across Theorytabs; Plus account subscription is not necessary, but instead of searching in the database they could load this .hkt file directly.
Both add4 and #5 have appeared in the public database, but I believe @Hooktheory has made even more now-nonfunctioning extensions.