Sorry I'm late to this thread, I was painting in the basement. No kidding!
Sounds like hiring an organizer is the right way to start, then having a cleaning crew on a regular will work wonders. Being the good project person you are just run with the "plan" from the organizer and you'll have this licked in no time. Save the basement for last because of the litigation but don't let that stop you from starting.
I've made quite the project out of my house over the years and today is the thirteenth anniversary of settlement. This year was the remodel of the master bath with travertine and a new roof replacing the nineteen year old original. I had three basement windows replaced and I was painting the trim just today. Funny timing on your thread!
One thing that worked wonders for me was purging crap that I don't need anymore. I hired the 800 Got Junk folks and they carted away half a truck full of carp I don't need, want or use anymore. It feels great to purge crap.