  Many of the short-lived radioactive nuclei that were present in the early
Solar System can be produced in massive stars. In the first paper in this
series (Brinkman et al. 2019), we focused on the production of $^{26}$Al in
massive binaries. In our second paper (Brinkman et al. 2021), we considered
rotating single stars, two more short-lived radioactive nuclei, $^{36}$Cl and
$^{41}$Ca, and the comparison to the early Solar System data. In this work, we
update our previous conclusions by further considering the impact of binary
interactions. We used the MESA stellar evolution code with an extended nuclear
network to compute massive (10-80 M$ _{\odot} $), binary stars at various
initial periods and solar metallicity (Z=0.014), up to the onset of core
collapse. The early Solar System abundances of $^{26}$Al and $^{41}$Ca can be
matched self-consistently by models with initial masses $\geq$25 M$_{\odot}$,
while models with initial primary masses $\geq$35 M$_{\odot}$ can also match
$^{36}$Cl. Almost none of the models provide positive net yields for $^{19}$F,
while for $^{22}$Ne the net yields are positive from 30 M$_{\odot}$ and higher.
This leads to an increase by a factor of approximately 4 in the amount of
$^{22}$Ne produced by a stellar population of binary stars, relative to single
stars. Also, besides the impact on the stellar yields, our 10 M$_{\odot}$
primary star undergoing Case A mass-transfer ends its life as a white dwarf
instead of as a core-collapse supernova. This demonstrates that binary
interactions can also strongly impact the evolution of stars close to the
supernova boundary.
