But did you start with the idea that the US and Rome are linked, then apply the dates, or did you look for events 2147 years apart and then make the connections fit?

Either way, you have to establish some form of connection between Rome and the US that can be verified from outside your idea. Verified isn't just a string of thinks like other things. Start with that.

Show a definitive connection between Rome and the US that is not shared by any other nation/empire.

I'd also suggest you look through the threads started by Dutch on his hyper-dimensional design thing. This is very similar.

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A Nerd can figure out how long it will take the original Enterprise traveling at warp 6.5 to travel from Regulus to Antares.
A Geek will think he can use that to pick up a girl in a bar.
A Dork knows he can't pick up the girl with it, but will hang around for hours anyway, just in case she asks.
She might. You never know.