Dig the stump out, and fill the hole with stone and stone dust. Once that compacts, it is as strong as concrete itself. The one thing that I have learned over the past 50 years, is that the best compaction is nature. After you dig out the stump, let the ground settle over one winter, and then do your concrete work. If not, no amount of rebar is going to keep the concrete from cracking. Rebar only keeps the cracks from opening up. A few years ago, I was involved in the "restoration" of a large department store that the floor had failed. When we cut open a section of floor, we could clearly see that the ground under the concrete had sunk about 3 feet because the trees that were cut flat with the ground had rotted away. The entire store had to be emptied of all merchandise and shelving, and a hole cut into the side of the building. Then we brought in jack hammers to remove one half of the floor. Once all that was put to one side, then the excavators came in and dug down 15' to remove all organic material. All the excavated material had to be trucked away, and clean organic free material was brought in and compacted in 6" increments until it was brought back to grade. I was told that the total cost was over a million dollars when finished. Now, there is a super market on the site, since the department store moved to another location. When it comes to construction, there are no short cuts that are successful over the long term. Do it right the first time, or keep repairing the shoddy work for years to come.