I think that in the rested XP areas that have boarding (ie Golden Tankard, Junction Inn) that they should have a room that is like your "character's room" in that establishment that still allows rested XP and also has a chest to access your stash like that of the dorm room that is in the Arcane Sanctum.
And I'm not saying to add sleeping quarters in all rested XP areas. Just make one of the rooms in the already existing rested xp areas a solo instance.