HYou can try this:

ListContourPlot[Select[phir4z0, 0.000098` < #[[2]] < 0.999945` &],
 GridLines -> Automatic, ContourLabels -> True, 
 ColorFunction -> "Rainbow",
 ImageSize -> Large, PlotRange -> {{0, 50}, {.05, .95}},
 PlotRangePadding -> None, AspectRatio -> 1/2]

I don't know that they qualify as jittery, exactly. Try ListPlot3D[Map[Reverse, allres]] to see what I mean. They really show a precipitous change I would describe as a fold, with some jaggedness on one side.

Some trial and error indicates that smoothing the middle coordinates can make a difference to the outcome. I show this below. I use a (fairly long) triangle-type filter to convolve those values.

offset = 17;
ker0 = Join[Range[offset], Range[offset - 1, 1, -1]];
ker = ker0/Total[ker0];
newy = ListConvolve[ker, allres[[All, 2]]];
{newx, newz} = Transpose@allres[[offset ;; -offset, 3 ;; 1 ;; -2]];
newpts = Transpose[{newx, newy, newz}];

ListPlot3D[newpts]

Now the contour plot.

ListContourPlot[newpts, GridLines -> Automatic, ContourLabels -> True,
  ColorFunction -> "Rainbow", ImageSize -> Large]

Still a bit of weirdness at the lower right but much of the jaggedness is gone. One can experiment with the kernel size to get a trade-off between smoothness and fidelity to the original.

Your data has a lot of points that are stacked vertically. I would exclude them:

ListContourPlot[Select[phir4z0, 0.000098` < #[[2]] < 0.999945` &],
 GridLines -> Automatic, ContourLabels -> True,
 ColorFunction -> "Rainbow", ImageSize -> Large]