We spent 5.5 hours doing just that this past weekend. It was really annoying work, but it had to be done before it got too hot. We had to first remove some of the flat boards that were covering up the soffit so we could get to them. Then we basically worked in stages and piled the insulation into the middle. Then we'd cover whatever we just uncovered with plastic, staple it down and put some of the insulation back so we'd have some room to work with.
Somehow, the fiberglass still got through my gloves, because my left hand felt all tingly and numb for about 2 hours after we were done. Its a really weird feeling.
Next step is to demo the soffit from inside the kitchen. Which is still going to create such a mess.