Okay, so this is a solution that was created by Star Wars enthusiast, fan fiction author and probable virgin* Kevin Anderson. The dude wrote the Jedi Academy Trilogy in 1994, and in it he describes the Kessel Run in vivid detail.
According to Anderson the Kessel Run is a route from Kessel to the area south (let's say Space South) of the Si'Klaata Cluster. He claims that the run, normally around 18 parsecs, is a dangerous one because of numerous imperial star destroyers and this nefarious being known as the Maw: a Black Hole Cluster.
Now, the Maw is supposedly a relatively stable cluster of black holes built by an alien race to harness energy, but they're still fucking black holes, so if you get too close to those buggers you're going to get sucked in and spit out probably in a J.J. Abrams movie... SO a ship that can fly close to the black hole cluster but still have the speed to escape the event horizon is going to be a much faster ship. And considering that the closer you fly to the cluster the faster you have to go, it makes sense that Han Solo would boast "It's fast enough for you old man." The Millennium Falcon had to have been going like Mach 40 or some other speed that would make a ridiculously dangerous gillette razor for it to escape. It solves Han Solo's seemingly odd speed claim about a measurable distance, and also takes into a count the speed of the ship.
Well... seems like everything is wrapped up all nice and...
BUT HERE'S THE PROBLEM WITH THIS THEORY!
What the fuck is a stable Black Hole Cluster? There's only one black hole cluster ever reported in space and that thing is more volatile than Rip Torn after he's had a few and as dangerous as hoping your audience will get a joke about a piece of celebrity gossip that pretty much died down last month. It's also highly radioactive and is found at the center of a galaxy. I don't buy that there's an area where dozens of black holes (that can potentially rip the shit out of space ships) just hang out and their gravitational pulls and radiation are all nice and in harmony. NOT BUYING IT KEVIN ANDERSON!
Also, the Kessel Run is a trip from Kessel to the area south of Si'Klaata? Space south? Like... space South? That doesn't make any freaking sense. Luckily for them if they get there slightly Space North they can take Space 1-95 down a few Space States.
Also, okay I buy a ship getting ridiculously close to a black hole and not breaking apart. Metal is fucking metal, I can't break it. But I can cut a son-of-a-bitch. And man can only handle like 10 times the gravitational pull of the Earth IF HE'S LUCKY! So there are several limitations to how close Han could really get. Wookies I have no primary documents for.
Long story short, this is a silly theory. It is for people who don't want to believe in science.
*I know what you're thinking... but I'm just a [virgin].