How to Plot with non-orthogonal axes?

Question

Sometimes I would want to Plot simple functions on unconventional projection, but without specifying all the styling myself. If one looks at InputForm of a normal plot, all this would appear to be deep magic. Although on more complex scenarios I would want more than an affine projection, it is also a good starting point. Unfortunately even that with sensible grid lines and ticks labelling seems to be painful with the kludge I have found (yes, arguments are pretty arbitrary in my example):

ParametricPlot3D[{t, TriangleWave[t/4], 0}, {t, 0, 10}, 
 FaceGrids -> {{0, 0, 1}}, Ticks -> {Automatic, Automatic, None},
 ViewMatrix ->
  {TransformationMatrix[
    RescalingTransform[{{-8, 12}, {-2, 12}, {-1, 1}}]],
   {{1, -1, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}},
 PlotRegion -> {{0, 1}, {0, 8/2}}]

Are there any more sensible approaches to this without generating all the details explicitly?

The hacky method I use is to convert the result of e.g. Plot[] to an image, and then use Image(Forward)Transformation[] on it. — J. M.'s missing motivation, May 18 '20 at 15:02
@J.M. I forgot to mention that slanted text is not necessarily a feature I'm looking for... ;) — kirma, May 18 '20 at 15:06
Does this answer your question? How to create a plot with inclined axes? — MarcoB, May 18 '20 at 15:14
@MarcoB Unfortunately "not really" - large portion of the work needs to be done explicitly and FullGraphics featured there has serious bit rot that would need to be worked around... but it's good to link here anyway. — kirma, May 18 '20 at 15:42

How to Plot with non-orthogonal axes?

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