The key principle of managing up/across is that you manage the relationships with your boss and your peers. No doubt that takes a great deal of time while also leading your team. However, take the time to think much wider than those audiences.
You may not interact directly with executives in other areas of the business, but the odds are that your peers and your boss do. Which means they are considering them in all their decisions. In order to truly help them and build consensus, you have to think about those other leaders.
The best way to help you do this is to get to know how they interact with their bosses. Ask questions like "what are you boss' priorities?", "what are the key things you do to support and communicate with your boss?", and "How can I help you support your boss?"
In addition, tell them about your boss. Describe what persuasion tactics are most effective, the best ways to communicate, and what are your boss' highest priorities.
When you widen the lens, everyone benefits.