Useful to run the following on both local and remote, to get a sense of what's happening:

bridge monitor

VM, where eth1 is connected to the network I want to make my RPi appear in:

ip link add br0 type bridge up
ip link add br0 up type bridge
dhclient -r eth1 && ip link set eth1 master br0 && dhclient br0
ip link set eth1 down
ip link set eth1 up

Raspberry Pi:

ip link add br0 type bridge
ip link del br0
ip link add br0 up type bridge
ssh -o PermitLocalCommand=yes -o "LocalCommand=ip link set tap5 up master br0" -o Tunnel=ethernet -w 5:5 -t root@192.168.167.237 "ip link set tap5 up master br0"