In reply to Dave Flanagan:
Here's a scan of the Lonely Planet map
https://imgur.com/a/QG1oy . You can see that the high route crosses the main route in the middle. I don't see any point in taking the western part of the high route over the western part of the main route as it's not actually very high, although you could find your own high route as gav is suggesting, a little south of the main route.
For the eastern part of the high route, which interests me more, you can see this goes very close to Pingu. There's also another mountain, Taseeqqap Saqaa a bit to the northwest of Pingu which you could go for too. It doesn't look like either mountain would require crampons/ice axe in summer. I have a 1:100,000 map which shows that neither mountain is too steep, except Taseeqqap on the north side. I'm sure there would be no trail to follow on the high route and you would be wading through the low scrub much of the time, which would slow you down.
I have a flight booked to Kangerlussuaq on 13th August. Let me know if you want to discuss things further.