Here is a link to a separate post with pics of the handwritten vs. broadside copies I was able to find online.
The first pic includes a link to a National Geographic article which suggests that though it was drafted on 7/4, getting it in circulation and even getting signatures for the document was a fairly extended process, with several (7?) of the final signatures added at some uncertain dates following the August 2nd “signing date.”
The second pic includes a link to an incredibly thoughtful article written by a librarian on some of the process involved with circulating, getting agreement on, and signing the Declaration. For example, it looks like the version George Washington ended up using was read aloud to the troops, and only the first 54 lines remain (I like to think that Mr. Washington just got impatient at the length and “edited” it when he thought he had read enough :)). The article also suggests that one of the anti-counterfeiting watermarks seem to have included (I tend to think deliberate?) typos, which suggests some potential explanations for my question to me.
My question is more or less limited to the title (what’s the deal with those “s’s”?), but always happy to learn more! :)
Edit: Caught a typo. There might be more. :P
If you're referring to the Ss that look like Fs, they are actually the "long S", which is a common letter form in pre-modern typesetting.
See this question from a few years ago, Why is lower case “s” written as “f” in older English documents? with an explanation by u/Noble_Devil_Boruta