  In recent years, a class of compact objects called gravastars have drawn
immense interest as regular solutions to end state stellar collapse. Since the
energy density involved in collapse process is expected to be high, it is a
natural choice to study such compact objects in context of modified gravity
theories which reduce to General Relativity (GR) in the low energy regime. We
have already framed a model of gravastar in such a modified gravity framework
involving extra dimensional Randall-Sundrum (RS) single brane gravity~[Phys.
Rev. D \textbf{102}, 024037 (2020)] \cite{Sengupta1}. As a sequel in the
present paper we substantially improve our previous model by choosing the
Kuchowicz function as one of the metric potentials, which leads to many new
interesting results and physical features from our analysis as discussed in
this paper. Also, we provide essential additional stability checks on our
gravastar model to investigate the possibility of any instability creeping in
due to the higher dimensional framework. Our present improved gravastar model
is found to clear all the stability checks successfully. Very interestingly,
the static spherically symmetric matter distributions are found to accommodate
both classes of solutions obeying and violating the modified energy conditions
on the RS brane as we find in this work. We can conclude from our analysis that
the Kuchowicz metric potential is very effective for describing regular
solutions to compact objects at substantially high energies on the 3-brane.
