While keeping in mind that I have brewed exactly 2 batches, I figured I would chime in with my experience. My first brew was a Brewers Best Cali Ale kit and that came with Nottingham dry yeast. I did not re-hydrate, just pitched dry. I had similar results as you describe, OG was 1.06 and FG was 1.02. I tried swirling, racking to secondary, but did not repitch. I figured I was only a couple points off the high end of the kits FG (1.016 I think).
My second brew was an Imperial Stout from morebeer brewed Sunday afternoon. OG was 1.09
. I used a White Labs liquid vial with a starter (look for a thread titled mason jar starter I think). The fermentation has been going strong since Monday AM. I have high hopes for this one completing to a decent FG. The first brew had died down pretty much within 48 hours.
If the FG turns out how I expect, I think I will be using liquid with starters from now on. I am a believer.