It is technically possible to convert your track record to a road in JOSM, it is however not the encouraged way. If you have already made substantial effort to improve the track this could be an exception so here is how you do it:
1. Open track in JOSM
2. Download OSM data from the area around
3. Right click the gpx trace in the layers' list (top right corner by default) and choose "Transfer to data layer" (or something similar I am not using english translation)
4. Use "Simplify way" (Shift + Y)
5. Manually delete any duplicate recordings, make sure you connect the new road where it sould be connected (junctions) and resolve any collisions (river crossings => bridge) and tag the new road... This can be done in PotlatchPotlatch
6. Upload the result