I'm a big believer in keeping in the lower end of the yeast's temperature range to minimize potential off flavors. Several mentioned a diacetyl rest, which is also important, as the yeast will clean some things during that, preventing diacetyl from forming later on. Now...yeast will clean up some other off flavors, too, after the majority of their visible work is done. To that end, I am not a believer in a two week ferment--I now leave all styles in the primary for 30 days. I will lower temps back down to the lower end of the yeast temp range after the diacetyl rest and let it sit there for the remainder of the month.
If you are having a lingering sweetness, it could be fermentable sugars or nonfermentable sugars. For the former, starting off with a strong and viable yeast stock is most important. Additional help can be given by adding a yeast nutrient to the end of the boil and hitting the wort with some pure oxygen twice during the first twelve hours. Also...roust the yeast each day for that first week or two by swirling/rocking the keg. If nonfermentable sugars or unconverted starches are your problem, it could be the length or temp of your mash steps. Longer doesn't hurt. Do you perform an iodine starch test? I know a lot of people don't bother with that, but I get at batch every so often where it takes twice as long for a given mash step to pass the starch test.
One more thing...you are using large starters. If you are not growing your starters at the lower temps of the yeast range, you are getting a lot of flavors in that starter and dumping two liters into five gallons of brew will have give a taste addition to the cleaner styles of beer...cold crash the starter and pour most of that liquid off before adding the yeast to your wort.
Many have contributed a lot of good inputs and, while they may all be small, they all add up to better beer in the long run. I remember trying my first brew years ago and was just thankful it was drinkable
Over the years, I think my beers have improved not just because of a single added step, but by incorporating many little ones over the years and trying to roll them into each brew. Temperature control is big one and you already have that in your repertoire, so that is great. I didn't get to that level for a couple years!
