AHC: Make Scranton, Pennsylvania's presidential street grid accurate

When the city of Scranton, Pennsylvania was first being laid out in the 1850s and 1860s, the decision was made to name the north-south avenues after the US presidents, in order, starting with Washington Avenue and going eastward up the hill on the city's east side.

So the avenues, as one travels east (say, up Mulberry Street), are Washington, Adams, Jefferson, Madison, Monroe, Quincy (for J.Q. Adams), and then...
Clay Avenue. And that's followed by Webster Avenue. (One senses there was a hardcore Whig on the Scranton City Council.)

The remaining avenues after Clay and Webster, going up the hill until the grid ends at Nay Aug Park, are: Taylor, Irving, Prescott, Harrison, Wheeler, Colfax, and Arthur.

So your challenge, if you choose to accept it, is to come up with a logical US presidential succession that would make the Scranton street grid accurate all the way up the hill.
 
Irving??? Prescott??

Wheeler, Colfax, and Arthur are post-ACW; Wheeler is out of order.

Harrison?? William H. was skipped over, and Benjamin is way early (unless the street was renamed later).
 
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