First, we are only looking at the American coin
My experience, gumtree absolutely sucks when it comes to PMs. Every seller wants a fortune. It's a fool's errand. Not long ago, there was a particular coin I was after and it just happened to be, in all of Gumtree Australia, in the town I was in, but the vendor wanted $500, when his item was written gEF on one side and aUNC on the other, in the photo. Of course his view was it was aUNC, but even at aUNC a shop-based dealer was 20% cheaper and the dealer has issues like overheads and GST. That is why I never go to gumtree for PMs, it is loaded with sharks and braindead idiots.
Rant over.
Now, the american coin.
Emotive story "given to me off my grandmother". Seriously, why say this? In my experience, sellers who pull family strings in there are manipulative. If so desperate, why not go to a dealer & get a valuation if they are worth that much? Because, maybe already this was done and most likely, they are not, hence now the plea for a salad veggie to save the day in gumtree.
The 1803 is struck in an almost horizontal manner. It would be best to determine whether the genuine article conforms to the curve of the circle of the coin.