Prototypes are starting today with the eth1 code as is with the plan to keep the interface nearly the same but swap in statelessness when ready.
As for deploying to production – the ideal is deploy stateless eth1 to eth2 as it would reduce the overall requirements on normal validators and users, but depending on relative timelines, it might be considered to deploy eth1 as is (without statelessness) to eth2. This would put the burden of the entire eth1 state on all validators/users and drastically change the base-line requirements to run eth2. Agreed though that such a compromise might be worth it depending on eth1x progress.