A renormalization-scale-invariant generalization of the diagonal Fade approximants (DPA), developed previously, is extended so that it becomes renormalization-scheme invariant as well. We do this explicitly when two terms beyond the leading order (NNLO,~j) are known in the truncated perturbation series (TPS). At first, the scheme dependence shows up as a dependence on the first two scheme parameters c2 and c3. Invariance under the change of the leading parameter c2 is achieved via a variant of the principle of minimal sensitivity. The subleading parameter c3 is fixed so that a scale- and scheme-invariant Borel transform of the resummation approximant gives the correct location of the leading infrared renormalon pole. The leading higher-twist contribution, or a part of it, is thus believed to be contained implicitly in the resummation. We applied the approximant to the Bjorken polarized sum rule (BPSR) at 0=5 and 3 GeV2, for the most recent data and the data available until 1997, respectively, and obtained af5(A/|) = 0.119lo:So6 and °-113-aoi9' respectively. Very similar results are obtained with Grunberg's effective charge method and Stevenson's TPS principle of minimal_sensitivity, if we fix the c3 parameter in them by the aforementioned procedure. The central values for a(M\) increase to 0.120 (0.114) when applying DPA's, and 0.125 (0.118) when applying NNLO TPS. ©2001 The American Physical Society.