As someone that is from that neck of the woods -
The weather begins to turn late September time. My advice (remembering Scottish schools are ahead of England's) would be to head up late August or early September. You could also shoot for before summer - anything mid-April time onwards is doable.
Off to the east is a bit meh... some spots are quite nice but a lot of it is fields, and it's hardly the 'highlands' as you've said.
The west (I.E. Fort William, etc) is pretty packed now, and late September is pushing it with the weather over there IMO.
The typical NC500 is a bit of a car crash now (pun not intended). Somewhere like Skye has been absolutely devastated by the building of that stupid bridge - what used to be a reasonably quiet and stunning place is now a tourist trap, full of coaches and those fu***** motorhomes.
My suggestion, if you wanted to enjoy as much of the 'highlands' as possible, would be to aim for mid-September time, splitting your trip between somewhere in the Cairngorms, and somewhere like Ullapool. Around Ullapool is still doable (think Lochinver or Gairloch), and you should miss most of the tourists by then. There are some very nice roads too.
If you drop a few things you might like doing (local history, fishing, whisky, sheepskin rugs, fighter jets, mountain biking, shooting, walking, photography, foods, dolphin spotting, looking at the views, etc) I'm sure I might be able to suggest a few more bits to do/places to swing past.
Have your wits about you on the roads though. The A9 is not a safe road to drive (it looks fine until someone in a rented motorhome pulls out of a T-junction in front of a someone) and people are absolutely clueless on how to drive the roads in the north. I had a lovely exchange with a Swiss bloke in the summer who thought it was appropriate to stop on very fast road (locals do 70+), on a blind bend, in the middle of the carriageway, to take a picture of a cow.
The other thing to note is that, rather amusingly, the NC500 route really isn't that nice. Yes, the views are stunning. However the roads themselves, whilst nice on google maps, are a very rough, hardy tarmac that isn't the best to drive your 992.1 GT3 on. They are full of tourists, logging lorries and the like. The first time I drove up there was in a hire car, and I'd cracked the windscreen about 5 miles outside Ullapool. Certainly, if you're after views and whisky, then that's the place. If you're after driving roads, I would be inclined to look elsewhere.