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In previous work we identified a population of 38 cool and luminous variable stars in the Magellanic Clouds and examined 11 in detail in order to classify them as either Thorne-Żytkow Objects (TŻOs, red supergiants with a neutron star cores) or super-AGB stars (the most massive stars that will not undergo core collapse). This population includes HV\,2112, a peculiar star previously considered in other works to be either a TŻO or high-mass AGB star. Here we continue this investigation, using the kinematic and radio environments and local star formation history of these stars to place constraints on the age of the progenitor systems and the presence of past supernovae. These stars are not associated with regions of recent star formation, and we find no evidence of past supernovae at their locations. Finally, we also assess the presence of heavy elements and lithium in their spectra compared to red supergiants. We find strong absorption in Li and s-process elements compared to RSGs in most of the sample, consistent with super-AGB nucleosynthesis, while HV\,2112 shows additional strong lines associated with TŻO nucleosynthesis. Coupled with our previous mass estimates, the results are consistent with the stars being massive (~4-6.5M$_{\odot}$) or super-AGB (~6.5-12M$_{\odot}$) stars in the thermally pulsing phase, providing crucial observations of the transition between low- and high-mass stellar populations. HV\,2112 is more ambiguous; it could either be a maximally massive sAGB star, or a TŻO if the minimum mass for stability extends down to <13 M$_\odot$.