Clouds Rest first might make it easier mentally to see the Half Dome as only a ~4 mile side trip, instead of ~8 for CR. But HD first should avoid most of the crowds on the cables. Maybe less of an issue with the permits?
Was also wondering if taking the JMT instead of Mist Trail on the way up would make the hike any easier. I have always done Mist up but the extra mileage on JMT might be worth the easier grade. I will have a separate trip to see the falls anyways

