I vaguely remember something like it in Gothic-inspired drawings in Andrew Jackson Downing's books...odd on an Italianate house...and to see two of them on the left window!

It is really odd. All the double windows have a double steeple crosshead, except that first floor window, it would never have had a crosshead originally as it was a bay. I thought maybe it might be a builders trademark or something.
This is a neat sketch a local artist did of our house.
{{!gwi}}From House

The right term for the window toppers would be architrave or window hood. Italianates are noted for their heavy window hoods that extend down the side casings for some distance. Since your house has lighter details, architrave is the best term.

The bay roof treatment in the cute sketch would be called a cornice, because it is a discrete structure, not an applied trim.
Casey, stickler for terminology.

Casey, I appreciate you pointing out the correct terminology! I really didn't know how to identify the window hood since it is part of the overall window trim, not a separate piece. This will at least make my search more specific.

Here is a sketch I found in the David Rumsey historical map collection. It is the residence of Orson Kent, the home is in Burlington, same as mine. It has similar window hoods, however, they look to be separate from the horizontal window trim, almost like a pediment. Mine are not like that, but obviously the shape is similar. Doing a search on Orson Kent did not pull up any info on who built his Burlington residence, but interestingly, while I was at the register of deeds office researching my house, the land was purchased from Orson Kent just before construction began.
{{!gwi}}From House