Kavanaugh is a moderate (slightly to the right of Roberts, but to the left of Alito), but Gorsuch is not. Gorsuch is an originalist. He often votes with Justice Thomas, who is a quintessential originalist, in cases where other justices vote differently (see Tennessee Wine and Spirits Retailers Assn. v. Thomas, Flowers v. Mississippi, Lorenzo v. SEC, BNSF R. Co. v. Loos). Gorsuch and Thomas also often join their concurrences.
His opinion in Bucklew v. Precythe on what a “cruel and unusual punishment” in relation to death penalty means is pure originalism.
Yes, in some cases (mostly criminal) he votes with the leftist justices, but it’s only because he believes that criminal law should not be vague. It is a legitimate view from the conservative perspective because vague laws give the government too much power over the citizens. Justice Alito is the opposite because he seems to support “law and order” at all costs (for example he is unreliable on the Fourth Amendment).
Good summation on the justices. You must have studied them.