You say "U.S they usually run into a problem … "but it seems like the rest of the question, and forgive me if I'm wrong, that is"me I generally run into a problem … "I mean, have your players really raised this as a problem that is hurting your enjoyment of the game?
I have not played or genetically modified the Gumshoe or Cthulhu systems, but I know the mechanics and the adventure path in particular.
Out of place
I must say that a number of things you raise like OoC or dive break don't seem like such at first glance, maybe there is more to it than you say, but:
While reading and interpreting these tracks, the players are largely out of place. I give them an accessory, they read it and they discuss it.
This appears to be exactly what the character would do; I certainly can't see investigators finding a written clue that ruins it and throws it away. If the players say "I think …", "What if this means …", "Would you say that …?", Then I can't honestly say if this is the player who speaks or the character who Talk like they would both make perfect sense.
Mechanical shape cools work to break dive
I can't see this at all: you have to be in a safe place, time has to pass, or you have to be between stages, which means that you are taking a breather from your activities and this is exactly how people in real life it refreshes.
You refer to friends and family. Have you really played these friends and family with players in a way that allows players to connect with them? If not, they are just names in a phone book. Human beings don't care about strangers in an emotional way; that's why humanitarian organizations try to put a single face on disaster relief appeals. One person we can relate to is more important than millions we don't know.
Failure is One option.
As long as there are enough clues that the character is on a deadline and players still don't act with the proper urgency, they fail and the unspeakable horrors eat up their brains. In fact, this is the most sensible way for a Cthulhu campaign to end.
However, don't underestimate how difficult it is to interpret tracks: they seem easy to you because you have the answers. Subtlety is not your friend here: even if you give them a calendar with a red circle around the 12th day and a big label that says "END OF THE WORLD DAY!" At least half of the players will lose it, forget it, or think you're playing with them.
Personally, I think that the character should find such a calendar and should put it in a prominent place, crossing out each day as they waste it. Even then sometimes you they have to break the character and say "Look guys, I mean it, the world ends on the 12th, you can flap around here if you want, but you're just wasting your time."
As for the bad guys' reactions: go ahead! If players make decisions that will hinder their own progress, then your role as a GM is to enable what players do. If there are now 12 guards in one place instead of 4, let the character find a note saying "The boss says that [the party] is coming: they are the [place where they hit] two days ago, they triple the guard, I want 12 guys on call at all times! Signed [Underling No 2]. " This tells them that if they moved faster, things would be easier: it is still up to them whether they move faster or not.