Knotweed flow starts late August here — is chasing it worth keeping colonies boiling through the dearth?

Question for the late-flow chasers. Here in Małopolska the Japanese knotweed thickets along the rivers bloom from about late August into September, and the old-timers speak of it like a secret — dark reddish honey, almost buckwheat-ish, and the bees hammer it because nothing else is flowering. My problem is the gap: after the linden finishes in mid-July we hit a proper dearth, and my colonies naturally dwindle just when they'd need to be strong for knotweed. Keeping them boiling means feeding through August, keeping young queens laying, and fighting robbing at every inspection. So, 5th season, honest question to those who've done it: is a strong August colony worth the cost and faff for what knotweed actually yields, or is this one of those flows that sounds better in stories than in supers?