Sequentially number features (intersecting and non-intersecting) along linear path
We need to sequentially number features along a linear path. It's easy to number features that intersect with the route, but what about those that are not intersecting? See this graphic which illustrates how we need to number things, from west-to-east. This is a hypothetical screenshot, so I know the parcels don't look correct. Also we cannot assume that the route will always be in a one-way direction. Sometimes it'll be West to East and sometimes it'll be North to South, etc.
Create a route from the line. Create points at poly centers. Locate (point) features along the route, using a radius tolerance for the off-line points. This will give you an m-value for each point.
The point ID appears to be the incrementing integer you want. But even if its not, you should be able to create one easily enough from any set of points with ordered m-values
https://desktop.arcgis.com/en/arcmap/latest/manage-data/linear-referencing/locating-features-along-r...
Thanks for that recommendation, but centers are not always in order of feature. See this example:
In this example, the blue shape clearly comes first, but the center is to the "right" of the red shape, and therefore it would be ordered second using your method.
In that case, instead of using polygon centroids, use the polygons. LFAR will return a start and end m-value for each polygon.
Find the minimum m-value for each polygon, sort that list and then you have the new order ID.
