How else could the signing of the Declaration of Independence have possibly looked? It's not like we'd expect them to sign with their feet.
How We Got It Wrong:
Let's start with the date. No one signed jack on the Fourth of July. The committee that wrote the document presented it to Congress on June 28, at which point the Congress put it aside while they spent a few days debating if they had the guts to break off with England. It wasn't until July 2 that Congress came to a consensus and voted for independence. Then Congress spent a few days editing what was actually no more than the press release of the event, the Declaration of Independence. It just so happened that the final (unsigned) product wasn't ready for publication until the 4th, but by then Americans already considered themselves not-English for two straight days. The Declaration was like the wedding announcement published in the local newspaper a week after the actual ceremony. Or better yet, the divorce announcement, if people were tacky enough to publish those.
"We hardly talk anymore, and when we do, it's like there's an ocean between us."
As for the actual signing of the document, it took months. Historians argue that all 56 signers were never in the same room at once, and some of the representatives on the document hadn't even been elected by July 4. It wasn't until an August 2 session that John Hancock got the ball rolling with his signature, and other congressmen followed suit in the very tiny space that was left. But that process wasn't a one-day event either -- signers were still laying down their John Hancocks up until freaking November.