There are a couple of the classic "Campaign Archetypes" (a topic for an essay?) that I think may work. First is:
The Deadly Peril
Something is out to get the PCs, something bigger than them. You need to make it very, very clear that they cannot survive without working together.
Problem is, when one of them inevietably goes off on their own. To keep the party together you need to slap them down, and hard. This is a very delicate task and can go horridly wrong.
next:
The Patron
Give them an aim, something they can all agree on, and have someone with the power to make them work together. Someone they don't want to cross, but want to ally with. Given your party this could be grating, but with some of their connections a conspiracy within the law enforcement community could work.
Or,
Try Something Different.
Give them something to tie them together.
Normally this would be a lot less drastic than this party will require, but hear me out. It's gonna sound nuts...
Focus on a single character at a time. For one, maybe two sessions. In each arc one player takes on a sort-of-mentor figure, the rest take on various NPCs, perhaps multiple in a session (simple summaries are enough).
Play through their awakening.
The Trick is thus: The mentor figures are the same person, under different names, wearing different clothes. Don't mention this to the players.
The Twist: The mentor goes missing. They all have ways to contact them, and they find leads to the other players. In this arc jump around between characters a bit. If one goes to the a diner, have the others pass it on the way, play up the near misses. Finally, have them meet, having found, through their own investigations a solid lead who is not going to be mistaken for one of the PCs.
Now, you have a mystery they are personally involved in, and know that the others have a similar connection to it. If the players are willing to make the characters work, it should be enough.
A decade or so ago, I had this exact problem playing with new/young players. I came up with a few solutions that worked depending on the group/players. It's admittedly a hard situation because they would assume anything the GM explicitly mentions is usually important. There's one thing I want to ask, but let me answer your questions, first:
Explicitly Mention These Are Rumors
Does your party have a bartender they visit? A place to eat or drink? Make sure they hear these rumors and, in the same sentence, explain that any following up results in no additional information. If they insist on going either take a GM break to explain flat out that it's only a rumor and they'll get nowhere (and probably die) trying to chase it down right now.
Offer It In Ways They Can't Follow
Assume the Nameless Evil is affecting things minutely. Have the players overhear mentions of people's bones aching even though the weather isn't bad, how the crops seem to be less healthy this year, or how the smell in the air isn't quite right. As the evil gets deeper and deeper you can even mention hearing phantom screams in the air, an ever-present tingle on the skin, or just an uneasiness that sits in the stomach.
Mention It As Something That Happened In Between Scenes
Typically games do not play through every minute of a character's life. There are plenty of times where they are walking around, eating, or simply just standing there. Depending on the setting, you can simply say that while doing a thing they overheard some rumors.
For example, say they want to go to the market. As they go to the Special Shop you tell them "On the way to the Special Shop you overhear two merchant talking about animals being more hesitant to travel ." If they insist on finding out more...well, the merchants are no longer there.
Have Real Consequences for Getting Distracted
Simply have there be real consequences if they chase ghosts (as @gatherer818 originally suggested in comments). Maybe they run out of time on their main quest and now lose out on something. Perhaps a Terrible Thing comes after them because they waited to long to clean out the Den of Bad Guys.
Let me follow up with...
Why do they feel the need to chase these down so fast?
Are they new players? Are they not used to you GM'ing? It may be a simple case of needing you to guide them a bit on how you like to play. If they're more veteran players, maybe they're used to direct things and a simple talk will solve problems. Along with weaving those in, I explain to my players quickly that a clue will render no leads if I don't want them chasing it, and we go on our way. I find my players appreciate that more.
The overall answer is to get your players used to receiving information that isn't actionable. As I first mentioned, a lot of players are used to the mentality of if the GM says something about a thing then it must be important. Maybe drop extra world-building information, like about how the birds in the area sing with the morning, or how they can hear about a parent talking about their troublesome offspring. You can then begin to weave in the hinted exposition with the environmental details.
To bring up a previous example, "The hum of many conversations greets you as you enter the [insert public gathering spot]. Parents bemoaning their stubborn children, an old man complaining about his joints though there's no weather in sight, and fisherman comparing the size of their catch."
Best Answer
You never hint, ever. You tell it like it is.
Your chosen system does not fit the story you are trying to tell. As such, it is no big deal: you can run any game with any system. That said, a system will colour both how the players interact with the story and what they expect of the story. If I play D&D, I expect a fantasy magical land, not XII century Castile. If I player Metal Gear Solid, I expect to play Solid Snake, not some child soldier… In the same way, a combat heavy system leads to an expectation of lots of heavy combat. There is nothing wrong with subverting this but a word of warning to the players is essential.
Obligatory link to the same page tool which you could use as a session zero to avoid expectation problems. Another way is to state that you are subverting the system and combat might not always be either advisable nor necessary.
In your particular story, since the town is in a time loop, let the PCs shoot their way in and die. They wake up the next day. How long they keep that up before they realise it is not working is linked to how insane they are: doing the same thing over and over again expecting different results is the definition of insanity.