Replay/WMG

Cracking the paperweight the first heart attack is what started the replays.
It was a magical artifact. Jeff broke it with the phone after his heart attack - it "saved" him.

Jeff survived every heart attack.
We only see the Jeff that was sent back into an alternate timeline.

Meeting other replayers is what extends the "skew" further for everyone who replays.
Evidently replayers aren't supposed to know each other. The first four times, Jeff only skews a day or a week ahead. After he meets Pam it it goes to months for him, and a year for Pam. It gets worse the next year after meeting Stuart.

The story of the "Not this time" replayer who sent the letter from Australia could have been:

 * They always did things the same way and decided they didn't want to meet other Replayers in the end.
 * Saw how much Jeff and Pam screwed the timeline that run and decided they weren't worth contacting
 * Was a member or the leader of a group of replayers who voted not to make contact.
 * Was someone who had already been replaying from 1938 to 1963. They had only planned on getting in contact if they replayed again, but the next time around they weren't replaying (they were as oblivious as everyone else), and the ad was never placed to be noticed.

Any death that wasn't the heart attack in 1988 really would be fatal.
Pam was right about looking up airline accidents and avoiding them. During the timeline where Jeff and Pam's knowledge really changed things he/she died in a war/terrorist action and that is why they never contacted them the next time around.
 * Maybe the "not this time" replayer died as a result of the heavily-changed timeline.

Jeff and Pamela put an ad in the paper in 1989 to see if anyone new was replaying.
If only to see what investments they could follow for the rest of their natural lives.

The aliens really were causing the replays for appeasement.
The Cuckoolander Was Right! The aliens were unhappy with Jeff and Pamela's work, but the replay where they went public and thus caused worldwide violence made up for the shortfall and then some.