Issues with Neo-Euler font

I'm starting this issue to handle the problems found with the Neo-Euler font. Peter reported the following:

This font seems to have extreme slanting which we don't compensate for.

$f(x)$ -- very slanted f.

$x_d a_d$ -- first d touches a

$\xi^k$ -- xi touches k

$j^d$ -- d "feels" to be directly over j due to continuing the direction of the slanting of j.

something ${\mathscr{P}}$ by -- the caligraphic P touches the b of "by".

Stretchy parens are sometimes a bit thick in the center piece:
    <mrow>
        <mo>(</mo>
        <mfrac>
          <mn>1</mn>
          <mrow>
            <mn>1</mn>
            <mo>-</mo>
            <msup>
              <mi>z</mi>
              <mi>a</mi>
            </msup>
          </mrow>
        </mfrac>
        <mo>)</mo>
      </mrow>
There doesn't seem to be an italic "h".
    <mtext mathvariant="italic">&#xA0;otherwise,&#xA0;</mtext>