This answer addresses only your question "What is known about graph isomorphism for MSCs?".

It seems (to me) that

- A one-sentence answer to your first question is "Nothing is explicitly known about this, and yet in the literature results are waiting for you, notably results of Mader, with which you can prove that MSC admit practical isomorphism testing."
- Yet (without having looked into the matter closely), my conjecture is that isomorphism of $n$-vertex MSC can be checked in time polynomial in $n$, and even practically so, and the mathematical essence of why this is so is contained in

Wolfgang Mader : Minimal n-fach zusammenhängende Digraphen. Journal of Combinatorial Theory B, Volume 38, Issue 2, April 1985, Pages 102-117

Why? Very briefly, the reason for my conjecture is that

Mader gives a proof of *structural properties* of MSC (in the direction of 'tree-likeness of certain substructures' and also of *sparsity*), properties which you can probably put to use, if you **combine** these structure theorems with the very well studied topics of

isomorphism testing for bounded-degree undirected graphs

isomorphism testing for tree-like graphs

to write out a full proof of the above conjecture.

Sadly, it will not be possible for me to really work on this. However,

If you need help with the *German in Mader's article* only, that is easy, and I think I can help you with this, though if you have access to large search engines, the language should not be much of a barrier. Mader's paper is clearly written. (Detail which seems useful to point out: Mader writes '$E(D)$' for the *vertex* set of the digraph, presumably because the German for 'vertex' is 'Ecke', and '$K(D)$' for the arc set.)

As far as I know, regrettably, an English exposition of Mader's *proofs* does not yet exist.

Mader's *results* are *mentioned* in the nice monograph of Bang-Jensen and Gutin, but, sadly, a proof is not given.

I once started working out an exposition of these results of Mader's, yet, sadly, never finished.

Depending on what you like/have to do, working out a complete exposition and/or new proof of Mader's above article might be a useful project, for you and others.

Getting briefly back to the subject matter of Mader's article, my recommendation (no guarantee that it will really work out, needless to say) is that

- you start by focusing on 'Korollar 2' in loc. cit., specialized to $n=1$, which gives you a (to my mind) highly-non-trivial structure-theorem on MSC, and then try to exploit this statement to construct an efficient
^{1} isomorphism-testing algorithm for MSC.

Good luck.

^{1} _{ ....and maybe even practical...note that Mader's proof is written for every digraph, no 'hidden constants' or 'huge $n$' or the like.}