Plant ID based on a description? (Now with pictures)

I figure it's a stretch, but you never know...

I was walking along a stream bed with plenty of Persicaria hydropiperoides growing. In a few places is another Persicaria or Polygonum growing alongside it. It grows shorter, with a slightly more trailing habit with slightly wider, stubbier leaves. Both the P. hydropiperoides and this other plant had long, "stalky" type flowers. The P. hydropiperoides flowers were white and the mystery plant had pink flowers that were just a tad more compact. Any thoughts?

Update, see pics attached below...