You probably need to get out of the car, but will not need to go far. I was taking a landscape last year and didn't realise there was a red grouse in tree. 100/200 yards from the road. You could also listen for shotguns but probably not wise the get too close! Walkers will usually say if they have seen any.
They should still be around just a few less. Im going up with the wife for a few days so not a photography trip this time, but I will try to make it out for sunrise a couple of times if the weather is right.
Higgor Tor is a short walk, Curbar is a bit longer but still fairly short, with the added bonus of possibly seeing Red deer at this time of year. Early morning being the best time for both places.
Neither of these venues have shooting on them.
I visited last week, the heather didn't look as good as previous years when it was a sea of vibrant purple. It looked quite dry and frazzled (as my wife described it) by the recent hot weather. There is some patches of vibrant purple but large amounts of dry lighter areas of heather. If you got some sun it would probably looked better but unfortunately the sun was missing most of the time I was up there.