I think I contacted about 3 or 4 dealers, all of them local (within 30 miles). I ended up with one that was my best price.
Then I found CarWoo, and thought I would try my luck with them. They did a similar search, and contacted 5 dealers, two or three of which were the same ones I contacted.
Of the others, they were further away than what I was willing to deal with initially, but after seeing one offer a fairly significant savings over the other (about $750), I decided to take that offer to one of the local dealers.
They matched it, and I walked away with about $700 savings (after the CarWoo fee) vs. my initial offers. So in the end, I was definitely glad I went with CarWoo.
If I had to do it again without CarWoo (and I would now, apparently), I learned that I should open up my searches to not-so-local dealers just to get the best offer, then have a more conveniently located dealer match it. That is, unless you want to reward the best-offer dealer with your business, and it's not too much of a hassle.
But I was still able to get roughly the same experience on my own, just dealing with the dealers via email.