You've mentioned a couple of the main issues that could cause a stuck fermentation--underpitching, poor aeration, poor temperature control, etc. And Dean and Brewchez are both correct in that going with either of their suggestions isn't likely to do any harm, but I'm wondering if you may have scorched the wort.

Did you take turn the stove off when you added the extract? Was the bottom of the kettle coated in burnt wort when you were finished?

If the wort was scorched, you may have a high level of unfermentable sugars in the wort, and no amount of rousing the yeast, adding heat, adding more yeast, etc. can fix that.* You may simply end up with a high final gravity, and at 1.020 or so, it probably wouldn't be too bad (in the case of a stout).

In my early days of extract brewing I would add the extract with the stove still on, and I later learned that this was causing what I thought were "stuck fermentations". They weren't stuck, they were simply done fermenting. Changing my technique to turning off the heat completely when adding the extract and not turning it back on until the extract was fully dissolved helped greatly. Full wort boils can also help prevent scorched wort.

*Note: The only thing that "can" make unfermentable sugars into fermentable sugars is the addition of an enzyme like amylase or alpha galactosidase (Beano). However, I don't recommend even trying this, as you would have to pasteurize your beer at some point to stop the activity of the enzyme. This would be a topic for another post, but put simply, friends don't let friends use Beano (in homebrews).

Go Ahead

I often shake up my fermentors to keep the fermenters going. (Just learned that -or is the vessel and -er is the organism.) My technique is to swirl the whole carboy to get the yeast back in suspension. It's best done on the tail end of fermentation and I routinely shake my high-gravity beers to keep them going.

Pros

• Much reduced risk of contamination
• No oxygen exposure

Cons

• Stuff sputters out of the airlock & could get it your eye (-:
• You could break a glass carboy

I suggest keeping the temperature the same.

The best advice I can give is to still wait it out. 6 days isn't all that long for a brew where you only pitched a Wyeast pack and not a larger starter of yeast. I ferment normally for 14 days. If you can raise the temp to 70-72ish that will ensure the yeast wake up and push to completion if possible. Normally fermenting at 68F is a great idea, but if your yeast were sub-optimal, a little kick in the pants with a slightly higher temp might help out.