Greetings,
you wrote
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
How can I change the vertical order of articulation marks?....
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

See the notation Reference Section 1.3.1
Expressive marks attached to notes ....

and play with their positions in the following...
(it seems not to be absolutely straightforward :) )
NB I haven't considered the \mordent  \turn   \fermata
in this!

I hope this helps
Cheers
Bill

+++++++++++++++++++++++++++

\version "2.16.0"
musa = \relative c'' {
  b2 b

  b--
  b-.
  b->
  b-^
  b-+
  b-_
  b-|
  % 1   2   3   4   5   6   7
  % --  -.  ->  -^  -+  -_ -|
   b-- -. ->  -^  -+  -_ -|
   b-| -_ -+ -^ -> -. --
   b-^ -> -. -- -| -_ -+
}

musb = \relative c' {
  d2 d
  d--
  d-.
  d->
  d-^
  d-+
  d-_
  d-|
  % 1   2   3   4   5   6   7
  % --  -.  ->  -^  -+  -_ -|
   d-- -. ->  -^  -+  -_ -|
   d-| -_ -+ -^ -> -. --
   d-^ -> -. -- -| -_ -+
}

\score {
  \new Staff { \musa }
\layout { ragged-right = ##t }
}
\score {
  \new Staff { \musb }
\layout { ragged-right = ##t }
}

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