Limes Avenue is emergency vehicles only (plus foot and bicycle) according to an approved Planning Application at https://governance.enfield.gov.uk/documents/s64084/FINAL%20Trent%20Park%20draft%20Committee%20Report_LBC.pdf which also confirms Snakes Lane, although private property, is the correct route for the approved developments. I've made some corresponding changes to the permissions on the two roads but it will take a few days to for OSRM and graphhopper to update so can't confirm if this works at the moment.