  As a continuation of the study (in arXiv:2102.07696 and arXiv:2104.12625) of
strong-coupling expansion of non-planar corrections in $\mathcal N=2$ 4d
superconformal models we consider two special theories with gauge groups
$SU(N)$ and $Sp(2N)$. They contain $N$-independent numbers of hypermultiplets
in rank 2 antisymmetric and fundamental representations and are
planar-equivalent to the corresponding $\mathcal N=4$ SYM theories. These
$\mathcal N=2$ theories can be realised on a system of $N$ D3-branes with a
finite number of D7-branes and O7-plane; the dual string theories should be
particular orientifolds of $AdS_5\times S^5$ superstring. Starting with the
localization matrix model representation for the $\mathcal N=2$ partition
function on $S^4$ we find exact differential relations between the $1/N$ terms
in the corresponding free energy $F$ and the $\frac{1}{2}$-BPS Wilson loop
expectation value $\langle\mathcal W\rangle$ and also compute their large 't
Hooft coupling ($\lambda \gg 1$) expansions. The structure of these expansions
is different from the previously studied models without fundamental
hypermultiplets. In the more tractable $Sp(2N)$ case we find an exact resummed
expression for the leading strong coupling terms at each order in the $1/N$
expansion. We also determine the exponentially suppressed at large $\lambda$
contributions to the non-planar corrections to $F$ and $\langle\mathcal
W\rangle$ and comment on their resurgence properties. We discuss dual string
theory interpretation of these strong coupling expansions.
