  The existence of a secondary (in addition to compact object mergers) source
of heavy element ($r$-process) nucleosynthesis, the core-collapse of
rapidly-rotating and highly-magnetized massive stars, has been suggested by
both simulations and indirect observational evidence. Here, we probe a
predicted signature of $r$-process enrichment, a late-time ($\gtrsim 40$ days
post-burst) distinct red color, in observations of GRB-supernovae (GRB-SNe)
which are linked to these massive star progenitors. We present optical to
near-IR color measurements of four GRB-SNe at $z \lesssim 0.4$, extending out
to $> 500$ days post-burst, obtained with the Hubble Space Telescope and
large-aperture ground-based telescopes. Comparison of our observations to
models indicates that GRBs 030329, 100316D and 130427A are consistent with both
no enrichment and producing $0.01 - 0.15 M_{\odot}$ of $r$-process material if
there is a low amount of mixing between the inner $r$-process ejecta and outer
SN layers. GRB 190829A is not consistent with any models with $r$-process
enrichment $\geq 0.01 M_{\odot}$. Taken together the sample of GRB-SNe
indicates color diversity at late times. Our derived yields from GRB-SNe may be
underestimated due to $r$-process material hidden in the SN ejecta (potentially
due to low mixing fractions) or the limits of current models in measuring
$r$-process mass. We conclude with recommendations for future search strategies
to observe and probe the full distribution of $r$-process produced by GRB-SNe.
