ggraph: Vertex position according to attribute

Suppose I have an igraph graph like the following:

library(ggraph)
library(igraph)

vertices <- data.frame(name = LETTERS[1:6],
                       time = c(0, 9, 9, 10, 10, 10))
edges <- data.frame(from = c("A", "B", "B", "A", "C", "C"),
                    to =   c("B", "D", "E", "C", "E", "F"))
graph <- graph_from_data_frame(edges, 
                               directed = TRUE, 
                               vertices = vertices)

For present purposes, the graph will always be a tree or a DAG, and I would like to use ggraph to plot the graph in a tree-like layout. My question is: How to plot this graph with the time vertex attribute for y-values?

I can set aes(y = time) in geom_node_point to correctly position the nodes, but the edges do not follow along:

ggraph(graph, layout = "tree") + 
  geom_node_point(aes(y = time)) +
  geom_edge_link() +
  theme_bw()

^{Created on 2019-11-17 by the reprex package (v0.3.0)}

Setting the y or yend aesthetic to time in geom_edge_link throws an error.

I am new to ggraph, so I'm stuck on how to proceed with this problem.