I don't think current TG (UK, obvs) hit its stride until about S4 or S5.
I've always maintained that the first episode of the "real" current Top Gear was 4x01. First Epic Race, first truly goofy car test with the Exige and Apache gunship. You had a few moments before that episode that had the current TG spirit (most notably the Hilux Destruction), and a few moments afterward that were holdovers from the first three series (nun in a monster truck, for instance), but 4x01 was the turning point. After that, the chemistry was there and visible and the formula was clicking. At that point, the Trio were together for 19 episodes. I'm willing to give TGUS the same amount of time to gel.
I think that, given time and a sufficiently long run, we might be seeing the Alaska trip as that same kind of watershed demarcation moment. If it's good, of course.
While the first three series had some good bits, what I've seen of it (mainly from S2 and S3; I've not watched any S1) was largely boring, IMO.
Agreed, and a lot of this was due to the format still being The Jeremy Clarkson Show With Special Guests Richard Hammond and James May, tacked on to a lot of the Old Top Gear format, which Fifth Gear was doing just as well or better (or so consensus opinion says). James was still doing those consumer advice bits well into S3.
I've been rewatching some of S1 lately, and, honestly, it's at the same standards of S2 and S3. The Jason Dawe Question, though, is still vexing. I think he was better at what he was doing than S2/S3 James. Would he have been allowed to expand his repertoire like James eventually did had he been kept on? Would he have had the ability to do so? James coming into his own is one of the key factors in what made New Top Gear a success. It's interesting to think about.