Can I use the original Rookery to shuffle Doomed events back into my deck?

No.

Every Doomed event is also Deathbound. Deathbound is a replacement effect that makes the event go "moribund:dead pile" instead of the usual "moribund:discard pile" after it resolves in Step 3 of the action window. The WES-Rookery's Response doesn't apply because the event is not headed to the discard pile when the Response could be triggered in Step 5.