Wendy, if you ever find out the area of Italy or Sicily your mother's father came from, and decide to bite the bullet and go there to investigate further, you will find that in Italy and Sicily, especially in the countryside areas, where the same families' descendants or their neigbours' descendant still live and work, having businesses etc, the locals know a lot about the old folk from the war era by name, and their stories. They can often tell you about people they remember, or have been told about, and who were prisoners of war, or who emigrated later, during the big emigration period.
This topic is close to my heart, as I researched my Italian American friend's family for him in Sicily, doing all the spade work for him beforehand, so in the end, with limited Italian resources online, to break down a brick wall, he went to Sicily for a week to get his grandfather's birth certificate in a village area. Whilst there he was chatting to a local cafe owner who told him all about his grandfather's family in the village, even though he'd never met him. It turns out that village life in Italy/Sicily, is much the same as in small villages in Ireland. Local ancestor knowledge is passed down by grandmothers,aunts,uncles and neighbours to younger members all through their lives. Call it gossip if you will, but it is very useful never the less.
My Irish descent mother passed on all her knowledge verbally to me about our wider family relations through time, throughout my life, which is how I was able to build our huge Irish family tree after she had died. These kinds of communities held family dear, and the family knowledge was very important to them, especially with not much else to talk about in remote villages. Not like today unfortunately.
Wendy, yes its a very good idea to build on the Italian trees you have started, however small and wide, because they will eventually act as a fishing net and will bring in more, wider matches to them. Eventually they could attract matches in the direction you need, closer to your grandfather's immediate family, which will then provide a solid surname. Without useful online Italian resources, the DNA numbers will help too, so keep your eye on the closeness scale numbers. Can't remember their technical name.
Meanwhile the connections you have to Bardi, which is in the Parma province, is exactly the kind of place where local knowledge will be abundant. Businesses like cafes, bakeries or ice cream parlours etc are often held and passed down through generations of the same family in Italy. So always start with asking those if you end up going once you have a solid surname for your grandfather. We passed by the top of Parma province, in Parma itself, on our foodie tour of Italy. Very easy area to travel through by car, lots of little roadside cafes have rooms to let above, no booking required. We just pointed the car and drove, and was never short of a place to stay, even at 9 pm at night. A lot easier than in France, and more affable natives, who ensure you go to bed full of Limoncello on the house, once they find out you are of Italian descent looking for your relatives!