  We consider $U(N)$ $\mathcal N=4$ super Yang-Mills theory and discuss how to
extract the strong coupling limit of non-planar corrections to observables
involving the $\frac{1}{2}$-BPS Wilson loop. Our approach is based on a
suitable saddle point treatment of the Eynard-Orantin topological recursion in
the Gaussian matrix model. Working directly at strong coupling we avoid the
usual procedure of first computing observables at finite planar coupling
$\lambda$, order by order in $1/N$, and then taking the $\lambda\gg 1$ limit.
In the proposed approach, matrix model multi-point resolvents take a simplified
form and some structures of the genus expansion, hardly visible at low order,
may be identified and rigorously proved. As a sample application, we consider
the expectation value of multiple coincident circular supersymmetric Wilson
loops as well as their correlator with single trace chiral operators. For these
quantities we provide novel results about the structure of their genus
expansion at large tension, generalising recent results in arXiv:2011.02885.
