I'm not sure there's an "easy" way here. I'd suggest that you connect up the MX to the cloud, and then run the Mgmt interface of the MS to the MX so you have a stable control plane to work with here. And then as you say, just migrate the L3 interfaces one at a time.
Moving DHCP is going to be a pain. I would suggest ahead of time you shorten the lease time on the MS down to something really short (1 hour? 30 minutes?) and let all your clients get the new short leases. This will ensure the clients re-dhcp to the MX within a reasonable period.