You find now in the Nepal Wiki-pages a tables of distances between several important towns in Nepal:
I hope the informations are usefull. The table structure still needs to be improved.
I uses Mapquest and OSRM to find the best routes (shortest time and not shortest length).
The distances to Taplejung are estimated because the town is in OSM no properjy connected with other towns. All routing software don’t route over “ford=yes” tagged ways. So parts of H18 for eyample are not used.