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Stars with an initial mass of $\sim 7$-11 solar masses form degenerateoxygen-neon cores following carbon burning. Electron captures in such cores cantrigger runaway oxygen burning, resulting in either a collapse or athermonuclear explosion. We provide a detailed description of the formalismused in previous work and apply it to two further forbidden transitions thatare relevant to degenerate oxygen-neon cores: the$4^+_\text{g.s.}\rightarrow{}2^+_1$ transition in$^{24}\text{Na}(e^-,\nu_e)^{24}\text{Ne}$ and the ${5/2^+_{\text{g.s.}}\rightarrow{} 1/2^+_{\text{g.s.}}}$ transition in$^{27}\text{Al}(e^-,\nu_e)^{27}\text{Mg}$. The relevant nuclear matrix elementsare determined through shell model calculations and constraints from CVCtheory. We then investigate the astrophysical impact using the stellarevolution code MESA and through timescale arguments. In the relevanttemperature range, the forbidden transitions substantially reduce the thresholddensities for $^{24}\text{Na}(e^-,\nu_e)^{24}\text{Ne}$ and$^{27}\text{Al}(e^-,\nu_e)^{27}\text{Mg}$. In the MESA models,$^{24}\text{Na}(e^-,\nu_e)^{24}\text{Ne}$ now occurs immediately following theonset of $^{24}\text{Mg}(e^-,\nu_e)^{24}\text{Na}$. The impact on the overallevolution is uncertain: this is due to known difficulties in accounting forconvective instabilities triggered by the $A=24$ electron captures. Thetransition between $^{27}\text{Al}$ and $^{27}\text{Mg}$ may have a minoreffect on the early evolution but is unlikely to affect the outcome. Thestudied transitions should be included when calculating weak interaction ratesbetween $^{24}$Na and $^{24}$Ne for temperatures$\log_{10}(T[\text{K}])\lesssim8.5$ and between $^{27}$Al and $^{27}$Mg for$\log_{10}(T[\text{K}])\lesssim8.8$.

Forbidden electron capture on $^{24}$Na and $^{27}$Al in degenerate oxygen-neon cores