Well before our visit, I made contacts with the UNESCO liaison office for Aasivissuit-Nipisat-it is a small group of 3 dedicated officers based in Sisimiut and Kangerlussuaq. 
One of them is the park ranger, Christian who patrols the area every day and calls it his office, exactly 585,000 football fields large! We rented a car (an adventure on itself to find it, price around 100 Euros) and Christian volunteered as driver and probably the best guide you could find, as he knows some hidden archaeological places along the road to the ice cap and Point 660. Like remains of hunting grounds, and places where the rendeer meat was dried before transport to the camps. As he works full time, he is normally available late afternoon. 
He can be contacted under chpj@qeqqata@gl
and one has to agree with him time and fees, but it is more economical than the organized tour, and the emphasis is the Inuit Hunting grounds, not the ice bergs. As we traveled privately, we could stop at any photo opportunity along the way which there are plenty. The landscape is amazing. 
Christian also has a fleet of 10 electric fatbikes which are offroad bicycles with oversized tyres, perfect for the long gravel roads and a sustainable way to discover the beauty of Greenland. In October 2024, the new road from Kangerlussuaq to Sisimiut should be opened, providing yet another opportunity to discover the UNESCO core zone in the opposite direction to the sea shore. You could bring your own tent or sleep in one of the huts along the way on the Arctic Circle Trail previously reserved for hikers.