I have a task that runs at boot that looks like this:
now=`date +%s`
# wait for influxdb..
until curl localhost:8086/ping &>/dev/null; do
sleep 1;
done
echo "Waited for indluxdb $((`date +%s` - $now))s"
#Restart homeassistant
docker restart -t 30 homeassistant
You should be able to add a sleep for say 300 sec. and do the same… Or try to connect to your most slow service and once that is up restart homeassistant. But, I think the hass.io guys have better solutions…