I stumbled into this group when trying to research some songs appropriate for Renaissance Faires (for English and Gaelic characters). A perfomer of children's songs told me this would be appropriate for the Renaissance Faires without any historical documentation. I'm very glad to see your group sites sources as much as you can.
I have two cents to add after reading the discussion. I believe that Heuchera are California natives (at least I remember reading of one in a book on California natives written by an author from UC Berkeley). According to the Encyclopedia Britannica, Convallaria majalis (lily of the valley) are natives of the North Americas (Eastern) and Eurasia.
So I'm going to make a dangerous assumption-leap that the song possibly stems from the North America's then (maybe??)? Or other places of colder weather (the huechera varieties I've seen in California wilt in the heat (triple digits) w/out a lot of water and shade and lily of the valley shrivel and will not bloom above temps in the 65 degrees farenheit range and hotter). I read someone's post about both being popular flowers since the 1700's though. I guess we really have to get a better date on the song to narrow down the location.
The other thing we have to take into account is that I'm sure there are other flowers known as "coral bells" or confused with coral bells. And I acknowledge that my assumption could be totally wrong since people may just plant them as annuals in certain places and replace them every year in the fall or winter.
Melodically/musically do we have a historical "trace" on the rhythm, pattern of the lines and/or tune? I'm not musically adept, other than I like to sing, so that type research is a bit beyond me.
Keep singing!