The road up through Altnaharra is an absolute cracker. Can't imagine why you'd want to miss it. The long climb from Lairg past the Crask Inn, then the descent to Altnaharra, and the rolling road up to Tongue... lovely. It's only the last stretch along the north coast that's a bit meh.
I haven't ridden the A9, but I remember looking out of the coach window on my way back down to Inverness from John O'Groats and thinking I was glad we didn't go that way.
Would also recommend taking the old military road from Fort Augustus along the southern side of Loch Ness, rather than the A82.