I wouldn't basically change the system that we have now. I think it could be made more efficient by senators making more use of the process of signalling to departments in advance what they're going to ask about and by the research staff briefing senators more thoroughly.
Senators, like politicians everywhere, are short of time. Time is of the essence, and you have to fit in with the times they have available. So basically I would improve the briefing process and the process of notifying departments in advance.