I don’t have experience with the Mapbox mobile SDKs, but would have expected that you can also use custom styles that point to other/your own services like you can do with Mapbox GL JS.

Using offline MBTiles seems to require patching the code according to OpenMapTiles.org:

Maybe see also Building a Navigation App using Open Source Tools - GraphHopper Directions API.

Isn’t YOURS super outdated? http://yournavigation.org/ says “Routing data from planet file: 2014-09-02”.

You probably are aware of the Routing and Frameworks wiki pages?

Maybe mapsforge/vtm would be an alternative, it seems to support multiple tile sources.

Ideally you would be hosting your own services (see also Switch2OSM) and the university might have the resources to do that. You then could also host the CyclOSM map style. There are plenty of open source routing/map/geocoding stacks to choose from. I guess the difficulty is to have the same routing engine and map style both on- and offline.

Or maybe you could collaborate with the University of Heidelberg that develops and provides Openrouteservice?