I wouldn't describe 20th of July as late - it's only 4 weeks from the longest day.

The only factor I would consider if you were going to make it much later is hours of daylight: the closer you're going to be to 24 hours the more the time of year is important. If you start in the period late May to mid July at midnight on a 23 hour schedule you'll be down on the road at Newlands before it's dark, which takes away some of the stress towards the end. I know of one or two attempts that failed because of navigational problems in the dark on the last descent.