Is this simplified consensus problem easier than the original?
What you're describing as simplified problem is usually called consensus with clean crashes.
You can just compute the maximum of all received messages once. To see that this is sufficient, observe that everyone receives the exact same messages after the first round. Thus everyone agrees on the same maximum value and all nodes decide correctly.

To solve crash-fault consensus on a general graph you need to assume $(f+1)$-connectivity. Then you could simulate each round of the FloodSet algorithm by flooding through the entire graph (taking $D$ rounds), yielding $D(f+1)$ rounds in total. I would be surprised if there's a more efficient way to do this (without additional assumptions on the graph, .e.g., high expansion).