Octonionic two-qubit separability probability conjectures

We study, further, a conjectured formula for generalized two-qubit Hilbert-Schmidt separability probabilities that has recently been proven by Lovas and Andai (https://arxiv.org/pdf/1610.01410.pdf) for its real (two-rebit) asserted value $frac{29}{64}$, and that has also been very strongly supported numerically for its complex $frac{8}{33}$, and quaternionic $frac{26}{323}$ counterparts. Now, we seek to test the presumptive octonionic value of frac{44482}{4091349} approx 0.0108722. We are somewhat encouraged by certain numerical computations, indicating that this (51-dimensional) instance of the conjecture might be fulfilled by setting a certain determinantal-power parameter a, introduced by Forrester (https://arxiv.org/pdf/1610.08081.pdf), to 0 (or possibly near to 0). Hilbert-Schmidt measure being the case k=0 of random induced measure, for k=1, the corresponding octonionic separability probability conjecture is frac{7612846}{293213345} approx 0.0259635, while for k=2, it is frac{4893392}{95041567} approx 0.0514869, ldots. The relation between the parameters a and k is explored.