Ignore most US before 1836. Before that the dies were made by hand with the stars or lettering being punched in individually around the central device so every die is different.
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It seems like a lot of work to create a galvano, master hub, master dies, working hubs, working dies, and then change it a short time later.
This method of die creation was not used until after 1868. The mint acquired a Hill reduction lathe in 1867. Before then they used Master die, working hub, working die. The master die would be created by sinking the central device from a hand cut hub and then the rest (except the date) would be punched in by hand. That master die then made the working hubs and would be used until it wore out (They may have reserved a few of the first working hubs to be used to create a new master die once the original wore out. That way one "Master Die" could be used for years even after the original on wore out.)
In the 19th century they may have also used the Pre 1968 method for new designs in their first year just in case their needed to be small changes. That is speculation on my part.
There are some things in early US that would fit what you are looking for. They are mostly design type changes,
Half Cents1793
Half Cent Liberty cap left 1793 only
Possibly 1802
Half Cent comes with rev of 1800 and reverse type of 1803
Large cents
1793 chain rev Mar 1 through Mar 12 1793
1793 flowing hair Wreath rev Apr 9 to July 17 1793
Liberty cap head of 93 used Sept 1793 and Jan 10 - 13 1794
Liberty cap head of 94 used Jan 17 1794 - Nov 12 1794
Liberty cap head of 95 may be too long in service for what you want last 4 dies of 1794 to July 1796
1839 Silly head used on 2 dies in 1839
1839 Booby head used on used on 9 dies in 1839
The Braided hair with head rotated counterclockwise may be too long for what you are looking for 1 die in 1839 to mid 1843
Two Cent Piece small motto, one die, actually a pattern die that was used for production.
Shield nickel rev of 1868 used for just part of 1868
I'm sure there are many others but I've spent enough time on this for the moment.