Yes, that’s the one I mean. In fact, it seems conceptually more complex to me. And you are right, the asymptotic worst-case complexity is potentially worse. But in experiments, FP (what they call DS in the PBFS paper) seems to always beat GGT (the other experimental paper), and PBFS seems to always beat FP/DS. And this is already on instances that are probably way bigger than what we need: Their smallest example has about 5k nodes and is done in 11 ms. Assuming cubic runtime, we might expect 500 nodes to run in less than 50 \mu s.
So it’s all about the constants, but they are also very dependent on implementation details. Your running time table is a great starting point. But it might turn out that for the instances we are interested in, the story looks exactly the other way round than asymptotics suggest. In fact, our instances are small enough that simple DS/FP with a nicely tuned min-cut algorithm might be the best solution.