SVG and DPI, absolute units and user units: Inkscape vs. Firefox vs. ImageMagick

I try to auto-generate an SVG file intended to be printed on a certain size (A4). I wish to use a path in it, which only allows 'user units', not 'absolute units'.

It seems to me that it is impossible to 'publish' an SVG file that has absolute units (e.g. document size) and a path anywhere, because I cannot get it to work properly across viewers.

Is there a way to get some consistency in rendering, like specifying a 'default DPI'?

Or put differently: Can I get my example below to render the same in all viewers without abandoning absolute units at all?

Related: Is there a way to force any of the applications below to render the image in the same way as one of the others? (E.g. I tried the -density option of 'convert', but I couldn't get the output to match Inkscape's or Firefox' output.)

Example:

I've created one SVG file, with three black squares (rect) with a red diagonal (path):

• Left: square and diagonal in user units
• Middle: square and diagonal in inch (seemed to me the most logical choice, but is not allowed)
• Right: square in mm, diagonal in user units

Which renders differently in different viewers:

• Inkscape: 90 DPI, all squares same size, red diagonal matches
• Firefox: 96 DPI?, latter squares to large (or diagonal to short)
• Convert: 72 DPI, latter squares to small (or diagonal to long)

Code:

<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<svg
   xmlns:svg="http://www.w3.org/2000/svg"
   xmlns="http://www.w3.org/2000/svg"
   version="1.1"
   width="200mm"
   height="100mm"
   >
  <g transform="translate(50,50)">
    <rect
       width="100."
       height="100."
       x="10"
       y="10" />
    <path style="stroke: #ff0000" d="M 10 10 L 110 110" />
  </g>
  <g transform="translate(200,50)">
    <rect
       width="1.111in"
       height="1.111in"
       x="0.1111in"
       y="0.1111in" />
    <path style="stroke: #ff0000" d="M 0.1111in 0.1111in L 1.111in 1.111in" />
  </g>
  <g transform="translate(350,50)">
    <rect
       width="1.111in"
       height="1.111in"
       x="0.1111in"
       y="0.1111in" />
    <path style="stroke: #ff0000" d="M 10 10 L 110 110" />
  </g>
</svg>

Inkscape (my default 'viewer'):

Firefox (note that the red line does not reach the lower right corner. I made a screenshot and cropped sort of arbitrarily):

ImageMagick (convert, no options besides filenames given):