I'm a U.S. native speaker. I've never heard anything like "after death the doctor." Michael's saying is common in a slightly different form: "they're locking the barn door after the horse is stolen." (The difference between "bolted" and "stolen" probably tells us something about U.S. and British national character--we must have more horse thieves).
Another expression is "a day late and a dollar short." That means that the effort was too late, and wouldn't have been enough even if it had been on time.
Expressions that mean something was almost too late, but not quite, include: "just in the nick of time," "got in under the wire," and "at the last minute."