There actually is a very workable way you can connect Harkenwold to the Gardmore Abbey adventure, and it's BECAUSE of the Red Dragon in MoGA ironically enough.
If you either are subscribed to DDI and can go into the Dragon Magazine archives *or* you own or can pick up the Dragon Magazine Annual 2009 hardcover book... there is an article called "The Longest Night". This is (I believe) the very first article written that gave any sorts of details about the Barony of Harkenwold. The article goes over a little bit of info about Harkenwold itself, and also gives the basics of an adventure plot-- a red dragon named Cazakk The Blessed has terrorized the villages of the barony by demanding tribute from them in the name of Tiamat. Right now the villages have to give quite a bit of their wealth and supplies on the winter solstice to this dragon in exchange for not getting destroyed. Baron Harken offers to make anyone who can rid them of this red dragon his actual heirs to the throne.
The several encounters in the article (not really a module per se, more just an outline) include Cazakk arriving on the winter solstice to claim his tribute, the party confronting him, Cazakk flying back to his lair if the party is too much for him and he's hurt, and then the party invading his lair to defeat him.
So what we have here is a red dragon who is threatening Harkenworld itself *and* a red dragon that appears in the Gardmore Abbey module (although I am unfamiliar with the module so I have no idea what that dragon's story is). All you would need to do is merge/change/combine these two dragons together so that it's a singular red dragon, and construct a reason why the red dragon from The Longest Night flies to Gardmore Abbey. Like perhaps Cazakk's lair *is* Gardmore Abbey, so that when the party beats him up on the night of the winter solstice, rather than fly into the Dawnforge Mountains to his lair (like the article suggests), he instead flies to the Abbey and the party then follows him (thus leading you right into that module). Or if you wanted to add some encounters to fill in the levels between Reavers of Harkenwold and Madness of Gardmore Abbey... you go through Reavers as written (while dropping hints of the village's additional money problems), then once Reavers is done you detail the arrival of the red dragon for tribute, with Baron Harken then offers his barony if the party gets rid of Cazakk. They confront the red dragon on the solstice, Cazaak flies away back to his lair in the Dawnforge Mountains, they then go on the road to invade his lair and try to defeat him a second time. But before they can kill him, Cazakk once again (gravely injured) makes his escape and flies to the Abbey thinking he'd be safe there to recover from his wounds. Thus the party can claim the treasure of the dragon's hoard, as well as return a lot of it to Harkenwold.
This Longest Night plotline and the invasion of the dragon's lair can take the party from 4 to 6... and when they return to the Baron, he tells them that if they can find and kill Cazaak for good... they will become his heirs. A little bit of sleuthing... the party discovers Cazaak hid out at the Abbey... and you are now good to segue into the Madness of Gardmore Abbey module as they go off to hunt Cazaak down.
I'm sure the whole thing will require a bit of massaging to get the plotlines to come together... but I do think it's cool that WotC created a perfectly viable adventure plot to tie these two modules together several years before either of them had gotten written. If you can get a copy of the article, I'd highly suggest checking it out. I ran the scenario for my players several years ago, and it was really, really fun.