Dear Linda:

Thanks for contacting the UVM Extension Master Gardener Helpline with your questions about Japanese knotweed. As you are aware, Japanese knotweed is a real problem in Vermont and we applaud your desire to tackle the problem on your property. 

We attach links to information about this plant and management options from the Vermont Invasives website (attachment #1), the UVM Extension Master Gardener (attachment  #2), and the New Hampshire department of agriculture (attachment #3). 

1. https://www.vtinvasives.org/invasive/knotweed-japanese

2.https://www.uvm.edu/sites/default/files/Extension-Master-Gardener/How_to_Battle_Japanese_Knotweed_and_Win.pdf

3.  https://www.agriculture.nh.gov/publications-forms/documents/japanese-knotweed-bmps.pdf

As these links explain, it is difficult to eradicate Japanese knotweed once it is established. We don't believe that you can use herbicides near the lake shore so you would have to attempt to control the knotweed through mechanical means (continual cutting and smothering). If you are successful in eliminating or controlling the plants by weakening them, you should consider using native plants as an alternative to the knotweed. The Northeast Regional Invasive Species & Climate Change (RISCC) Management Network notes that using native plants "can increase biodiversity" and "dramatically increase the diversity of bees, butterflies, birds and other animals. In contrast, non-native plants do not support local food webs and can become invasive." (link #4 below). 

Giant fleeceflower (Persicaria polymorpha) is not a native plant.
The Vermont Invasives website (link #1, under the tab "how you can help") recommends Common Buttonbush (Cephalanthus occidentalis) as an alternative to Japanese knotweed and includes useful information about other plants and shrubs native to Vermont. We also include a link to the Missouri Botanical Garden's factsheet about Common Buttonbush (link #5 below).

4.https://www.uvm.edu/sites/default/files/Extension-Master-Gardener/Regional_Invasive_Species_Climate_Change_Management_Challenge_.pdf

5.https://www.missouribotanicalgarden.org/PlantFinder/PlantFinderDetails.aspx?kempercode=g830

With respect to your question whether a non-invasive plant would compete or drive out the invasive, it is unlikely that a different plant could compete with the very aggressive Japanese knotweed unless you had taken steps to eradicate the knotweed or weaken it. 

You also asked  whether a different plant could cross pollinate and spread the invasive. Japanese knotweed (Polygonum cuspidatum) is a different species from Giant Fleeceflower (Persicaria polymorpha). We did not find anything that indicated they would cross pollinate.

We hope that this information is helpful. 

Good luck.

Pat