How to find Matano plane

Maybe I'm missing something but isn't the value for z just the solution of the equation

(z - xLimits[[1]])*yLimits[[1]] + (xLimits[[2]] - z)*yLimits[[2]] == area

where area is the total area under the graph, i.e.

area = NIntegrate[GetRLine3[{data}, 3][x], {x, xLimits[[1]], xLimits[[2]]}][[1]]

Therefore, z is equal to

z = (xLimits[[2]]*yLimits[[2]] - xLimits[[1]]*yLimits[[1]] - area)/
      (yLimits[[2]] - yLimits[[1]])

For a start it seems to me that you can use NIntegrate:

z = step = xLimits[[1]] + (xLimits[[2]] - xLimits[[1]])/2;

While[
  {part1, part2} = 
   Flatten[{
    NIntegrate[f - yLimits[[1]], {x, xLimits[[1]], z}],
   -NIntegrate[(f - yLimits[[2]]), {x, z, xLimits[[2]]}]
   }]; 
  part1 != part2, 
  If[part1 > part2, step /= 2; z -= step, step /= 2; z += step]
] // Timing

z

{0.14, Null}

10.3795