  The study of structures involving vortices in one component and bright
solitary waves in another has a time-honored history in two-component atomic
Bose-Einstein condensates. In the present work, we revisit this topic extending
considerations well-past the near-integrable regime of nearly equal scattering
lengths. Instead, we focus on stationary states and spectral stability of such
structures for large values of the inter-component interaction coefficient. We
find that the state can manifest dynamical instabilities for suitable parameter
values. We also explore a phenomenological, yet quantitatively accurate upon
suitable tuning, particle model which, in line also with earlier works, offers
the potential of accurately following the associated stability and dynamical
features. Finally, we probe the dynamics of the unstable vortex-bright
structure, observing an unprecedented, to our knowledge, instability scenario
in which the oscillatory instability leads to a patch of vorticity that harbors
and eventually ejects multiple vortex-bright structures.
