Burn It All Down – Britain, 1982-84

That's why I started with the KAL 007 crisis, as the deaths of two Senators and two Representatives would cause more anger in the US (and in the Reagan administration) and, here's another way to make tensions worse--if you believe the Soviet news agency Tass (and take it with a massive grain of salt, IMO--I don't buy it IOTL), former president Richard Nixon had been booked on the flight (he was to be seated next to McDonald, but decided not to go).  

So, let's have a former president, two Senators (who were ideologically aligned with Ronald Reagan--Helms was considered as a potential VP pick, but the Reagan camp felt it needed moderate voters with John Anderson in the race, which is part of the reason George H.W. Bush), and two Representatives killed in the KAL 007 shootdown.  This will, of course, increase tensions considerably between the Soviets and US. 

Then, in response to the death of the South Korean president (and the subsequent revelation that North Korea was behind the attack), the US begins calling up forces to send to South Korea in response (and in case the North Koreans decide to attack).  The Soviets, thinking that the US is mobilizing for an attack against them, start calling up their own forces in response.  Then, the Beirut bombings occur and the US, wanting to send a message to the Soviets (possibly because they found out about the Soviet callup), bomb the perpetrators--along with, unrelated to this, invading Grenada to overthrow the left-wing government there.  Then, the Soviets, due to all of this, think that the Able Archer exercise is an attack and decide to strike first...

Is that a good enough scenario?