Seems like we have now sorted out all the train travel...
When you have a bicycle with you the "Intercity" trains have many advantages. Not as fast as the Freccia, not as cheap as the Regional trains, but they have proper bike storage facilities!
We will use Intercity from Roma to Bologna and from Bologna to Faenza.
We will use Regionals from Narni to L'Aquila and then varying (depending on the day of travel) from Lecce back to Roma.