I'd think your best bet is to clone your points to a temporary layer and attempt to 'snap' the points to the nearest centerline, then use those temporary points as inputs for your routing.
You can use 'Generate Near Table' and some scripting to calculate the distance between the point and the line, and the vector along which to move the point.
I asked Google Gemini if it could write that workflow -- from the response, as it turns out, you don't even need any algebra in the flow, as the GenerateNearTable tool will provide a NEAR_X and NEAR_Y fields with the 'location' parameter. So if you're not comfortable with Python, you should be able to pull off a two-step 'model':
1. Generate Near Table (with location parameter); then, use the output with
2. XY Table to Point (using the NEAR_X and NEAR_Y).
import arcpy
# Define inputs
point_fc = "Original_Points"
line_fc = "Reference_Lines"
near_table = "memory/near_results" # Using memory for speed
shifted_output = "Shifted_Points_Copy"
# 1. Generate the Near Table with location coordinates
# The 'LOCATION' parameter ensures NEAR_X and NEAR_Y fields are created
arcpy.analysis.GenerateNearTable(
in_features=point_fc,
near_features=line_fc,
out_table=near_table,
location="LOCATION",
closest="CLOSEST"
)
# 2. Store coordinates in a dictionary {IN_FID: (NEAR_X, NEAR_Y)}
near_coords = {row[0]: (row[1], row[2])
for row in arcpy.da.SearchCursor(near_table, ["IN_FID", "NEAR_X", "NEAR_Y"])}
# 3. Create a copy of the points to avoid modifying the original data
arcpy.management.CopyFeatures(point_fc, shifted_output)
# 4. Use UpdateCursor to move the points to the nearest line location
with arcpy.da.UpdateCursor(shifted_output, ["OID@", "SHAPE@XY"]) as cursor:
for row in cursor:
oid = row[0]
if oid in near_coords:
# Update the point's XY to the nearest line's XY
cursor.updateRow([oid, near_coords[oid]])
print("Points successfully shifted to nearest lines.")
