I think your theory sounds good. I have filled/sprayed poly-urethane insulation a few times and my first question is why did the company that did the upper portions not want to do the lower?
The second concern is having loose material in the cavity I think will be a problem. Unless it is fixed in place I think it will float and move making it difficult to get the cavity full. The material that you will pour in is probably going to be pretty thick and it may not fill around the loose pieces as well as you think.
Remember to get an R-value of 6 you only need an inch of material. You don't need to fill some of those huge cavities.
What are you going to use as a finish on the lower walls? Can you build out a little and incorporate a rigid urethane board in the "furring" this might be an advantage when running electrical or plumbing not to have it encapsulated in permanent foam??
Good luck I love working out tough application problems like this.
jesseannie