Privacy Badger is also good for things like this: you can be logged into Facebook, but Privacy Badger will block requests to Facebook from third-party sites.
From my understanding blocking 3rd party JS is largely insufficient for accomplishing this, regardless of DNT settings.
You may be right regardless that it's better to appear as much like a stock browser as possible, in terms of privacy settings, so DNT should stay disabled. But in practical terms it might not make of a difference.
For a single browser session; this should work. Over months, it's harder. A tracker would needs to at least be quite aggressive and collect a lot of information to track you, and then be fairly clever in fuzzily matching that in the future if they want to track you over time.
Which isn't to say that short-to-medium term tracking is just fine, but it's not black and white either.
Your user agent plus unique plugin installations plus fonts installed equals a unique fingerprint across IP addresses. The above isn't an exhaustive list, either. There are dozens of tricks to track you.
Example: jQuery is sometimes hosted on Google CDNs. You can't block that request without breaking the site, right? But that request sends all your info.
And typically a request for something like jquery from a CDN will contain little more than your IP address and cookies. You can even prevent the cookies from being sent if you want. The only way they could get away with more than this would be to modifying the resulting script to grab more info from your machine.