Oh, in theory Reitti could function in such an environment. You would need your own tile server to display the map and maybe your own reverse geocoder. Then you can create your own map style (get an existing one and replace the source tile URLs) and point Reitti that way to your hosted services. It will be a lot of work and, depending on your needs, will need a lot of space.

For map tiles, I host an instance of openfreemap.org And for reverse geocoding, there is Photon or my own, Paikka.

If you want to follow up, let me know in a GitHub discussion. I could sketch out a way to do it, and maybe someone else could also use that information then.