I tried a search on newspapers.com to see if I could find a marriage announcement or obituary for Elizabeth, thinking it might list the parents, but I wasn't successful (you may have already tried this route).
My only other thought is that there is a Horn DNA project on Family Tree DNA that you could try contacting if you haven't already. https://www.familytreedna.com/groups/horn/activity-feed
I did check your Gedmatch number against mine, and we didn't share any DNA, unfortunately (sorry I can't help there!). My Horns didn't come to the U.S. until the 1840s, so it was a long shot with your Elizabeth being born in the 1810s, but it was worth a try.
Sorry not to be able to help more, and good luck with your search!