Having experienced poor conditions twice on the Haute Route in March I am wondering if a change of venue is in the cards.
This high level route has a reputation for the nicest huts, and the best early season conditions. The huts in this part of the Tirol open in mid-February as opposed to the March dates more common in Chamonix or Zermatt. The route is successfully guided quite frequently in March, and while not a scientific study, I can say that most of the videos posted on YouTube were from March trips.
As per possible peaks to bag, there are many, including Piz Buin, Silvrettahorn, and Breite Krone pictured here.