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:
Any death that wasn't the heart attack in 1988 really would be fatal.Oh, the person would still be alive, but they would be themselves from the original timeline, just like everyone else in the world who doesn't replay. 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.
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.