Summary: We conduct a pair of quasirandom estimations of the separability probabilities with respect to 10 measures on the 15-dimensional convex set of two-qubit states, using its Euler-angle parametrization. The measures include the (nonmonotone) Hilbert-Schmidt one, plus nine others based on operator monotone functions. Our results are supportive of previous assertions that the Hilbert-Schmidt and Bures (minimal monotone) separability probabilities are \(\frac{ 8}{ 3 3}\approx0.242424\) and \(\frac{ 2 5}{ 3 4 1}\approx0.0733138\), respectively, as well as suggestive of the Wigner-Yanase counterpart being \(\frac{ 1}{ 2 0} \). However, one result appears inconsistent (much too small) with an earlier claim of ours that the separability probability associated with the operator monotone (geometric-mean) function \(\sqrt{ x}\) is \(1-\frac{ 2 5 6}{ 2 7 \pi^2}\approx0.0393251\). But a seeming explanation for this disparity is that the volume of states for the \(\sqrt{ x} \)-based measure is infinite. So, the validity of the earlier conjecture – as well as an alternative one, \( \frac{ 1}{ 9}(593-60 \pi^2)\approx0.0915262\), we now introduce – cannot be examined through the numerical approach adopted, at least perhaps not without some truncation procedure for extreme values.