Max flow algorithm for floating-point weights and E~=10*V
Orlin's algorithm can solve max flow in sparse graphs in $O(|V| |E|)$ time.  See

Max flows in O(nm) time, or better.  James B. Orlin. STOC 2013.

You'll have to decide whether the potential speedup is worth the time to implement it, as I believe the algorithm is quite complex.  I don't know whether the algorithm is better in practice.

Perhaps someone else will have better suggestions for you.