@KentPfeiffer ... your wisdom is worth a lot in my book! I am really bad when it comes to comparing photo's for ID so mine are only suggestions as sorta looks like.
Natalie: If we have a general database entry for Persicaria you could upload a photo or two there and hopefully at some point someone would recognize which one it is and then it could be moved to the correct entry. I have a difficult time finding general entries in our database so hopefully if someone can find one they will link to it here on this thread.