Like you bnk, most of our camping has been done on the Eastern beach, but on our early trips to Moreton we camped a number of times at Ben-Ewa. Great spot for families, toilets, cold showers, water on tap and most of the time a calm beach. Ben-Ewa has only a small number of campsites that are set back off the beach...forget off hand but I think there is been 10 or 12 sites...years ago there were more, but a permanent commercial campsite on the left side of the ring road has been allocated for back packers who visit the island...not sure if they are still there, they were the last time I visited.
As for the mozzies and midgies, can’t ever remember them being too bad, I think early morning and late afternoon they were at their worst, but nothing a hat and some repellent didn’t fix.
Afternoon sunsets were great. Most days saw everyone trudge down to the beach with chair and a beer and watch the sun slowly sink down over the horizon...magic!