Showing strong connectivity is in DSPACE((logn)^2)
You don't need to pass $G$ every time, since it doesn't change across calls. You can think of it as a global variable, which is stored only on the input tape. The other parameters take only $O(\log n)$ steps, and since the depth of the call stack is also $O(\log n)$, in total this uses up $O(\log^2 n)$ space on the work tape.