How to make a simple network bridge in Vagrant?

I'm trying do set up the most basic network bridge demo in Vagrant. I have two machines in the same subnet, but on different LANs, and a bridge machine with two interfaces and a network bridge that gets set up in a provisioning script.

Here's my Vagrantfile:

$bridge_script = <<SCRIPT
sudo apt-get update
sudo apt-get install -y bridge-utils
sudo brctl addbr br0
sudo brctl addif br0 eth1 eth2
sudo ifconfig br0 up
SCRIPT

Vagrant.configure(2) do |config|
  config.vm.define "machine1" do |machine1|
    machine1.vm.box = "hashicorp/precise64"
    machine1.vm.network "private_network", ip: "192.168.1.2",
      virtualbox__intnet: "lan1"
  end

  config.vm.define "bridge" do |bridge|
    bridge.vm.box = "hashicorp/precise64"
    bridge.vm.network "private_network", ip: "0.0.0.0",
      virtualbox__intnet: "lan1"
    bridge.vm.network "private_network", ip: "0.0.0.0",
      virtualbox__intnet: "lan2"
    bridge.vm.provision :shell, inline: $bridge_script
  end

  config.vm.define "machine2" do |machine2|
    machine2.vm.box = "hashicorp/precise64"
    machine2.vm.network "private_network", ip: "192.168.1.3",
      virtualbox__intnet: "lan2"
  end
end

I can't get either machine to ping the other successfully. Using tcpdump I found that an ARP request get passed from machine1 all the way to machine2, but when machine2 responds, the response does not even get to eth2 on bridge. (I only see the ARP response when listening on eth1 in machine2.

How can I get this to work?