Directions/routing using custom geojson

Hello,

I'm trying to draw my own pedestrian paths in a big field and display this map on my website, allowing the user to enter a start and end point to get directions using the custom paths. I have created the geojson file using geojson.io, but I can't seem to find any mapping software/service that allows directions/routing using the geojson lines rather than the OSM data (roads, pedestrian paths etc.). Could anyone point me in the right direction? Ideally I wanted to do this in Mapbox as I've made my own custom map style, but I'll switch to anything that supports routing using custom routes defined by geojson. Thanks!

EDIT: Some additional info, I thought about updating the data on OSM but the custom paths I need to add are only relevant for a specific period of the year, the rest of the year the current OSM data (roads, paths) are correct. I wouldn't want to make these changes permanently for everyone, plus I made a small change and it didn't seem to reflect when I later tried doing some directions using Mapbox.