You sent me a PM asking for my detailed analysis of the relics to accurately date the site. Taking into account ALL of the relics, I believe the site was occupied from the very-early 1800s to as late as the 1850s.
The shoe toe-tap is the only item which dates that late. That particular kind does not come from early-1800s sites, but many have been found in mid-1800s sites.
I have to disagree about the raised-lettering "Double Quality" button being from the late-1700s ...because its backmark includes an indented wreath (hard to see in the photo, but it is encircling the lettering). That indented marking would push the button's date into the 1800s.
While on the subject of buttons... as I've mentioned previously, large quantities of British-made buttons had to be imported into the US until the "young" American button-making industry developed sufficiently to mass-produceenough buttons to satisfy the demand from the fast-growing American clothing industry. That finally occurred in the 1830s. The British-made 1-piece buttons can be distinguished by their use of British quality terms, lettering-style (font), and spelling. Note that one of your buttons has the words "strong gilt" written in fancy Old-English Script lettering ...and another of your buttons uses the British spelling "colour" for the word which we Americans spell as "color."
Since the majority of the buttons you've found at this site have British characteristics, but were dug in America, I would date them from the very-early 1800s through the 1830s. As I said above, the shoe toe-tap is the only relic which is younger than that.
The musketball's diameter indicates it was for a .50-caliber smoothbore musket, which dates from the Colonial era through approximately the 1840s. (That is also the time-period of your Pewter spoon-handle.) But in view of your other relics from the site dating from the first half of the 1800s, I think your musketballs and spoonhandle date from that same time-period.
