Then this is something to make a known for you. It’s something you need to build into your training between now and August.
This is one of those “it depends” when people ask how to train for LEL. Majority of training is just building the endurance fitness up. But with the sleep deprivation we have something you need to go and see how it kicks in for you, when it kicks in, and how you can deal with it.
You will have to head out and see how sleepy tired feels. As well as your 600, before then I’d suggest just heading out at midnight after a weeks work. Cycle through the entire night with a plan to be home by breakfast. Go find out how you cope through the night, when the dozies kick in, and how it progresses, You don’t need a big ride to make the dozies a known for you. One of the keys of long distance riding is recognising different types of fatigue early and dealing with them so they never become a problem.
Most I’ve done in a day on a mtn bike is the Ridgeway which is about 90 miles. A friend had leant out his mtn bike to another friend and so was on a CX bike. Boy was he sore by the end. On the mtn bike it was fine, time for a pint. My mtn biking was pre long distance riding. I did an off road coast to coast over 6 days in 2005 but that was only 30-50 miles per day.