We study excited states of two-quasiparticle (2qp) character in well-deformed even-even actinide and heavier nuclei exhibiting $K$ isomerism within the framework of the Skyrme energy-density functional (SEDF) approach, including BCS pairing correlations with self-consistent blocking. We use the SIII SEDF parametrization with time-odd terms and seniority pairing residual interaction as in a previous study of magnetic moments in odd-mass nuclei [Phys. Rev. C 91, 054307 (2015)]. The strength of the seniority interaction is determined through an overall fit on the $2_1^{+}$ excitation energies along the lines of Phys. Rev. C 99, 064306 (2019). Our calculations confirm the 2qp configurations reported in the literature providing an overall good agreement with the available data on isomeric energies. One notes, however, a few significant deviations such as in the $N=142$ uranium and $N=152$ nobelium isotopes, which are explained through known single-particle features of the SEDF used. Given the good predictive capability of the approach, we expect it to serve as a reliable tool in the search for similar kinds of qp excitations and to suggest additional or alternative qp configurations.