Well, this dead horse has been whipped quite a bit, but I haven't had my chance yet.
The only thing I can add to the "keep at it" advise is that on certain larger stumps, you may find it helpful to dig yourself one or two access lanes into the bottom of the excavation. I took out a 24" sycamore where that would have been a good idea. I kept trying to avoid the issue, but I was working on top of spoils piles and reaching far enough with the hoe that I lost some of my mechanical advantage. Even if it means a larger repair, if you have to go over 4 feet deep, it might be a good idea to get your machine down lower as your dig goes deeper. Oh, and the advice about keeping your spoils as far from your work as possible -- I'll second that one, too.
One more. If any of the trees are in the 6-8 inch range, and they're not down yet, I highly recommend not cutting them. I took our several large cedars by limbing them up as high as I could, digging out around the base like has been discussed here, and then pushing them over. I had an equal number that I had already cut, and the digs had to go much, much deeper.
Okay, really, last comment. Re: burying the stump. Depending on species, you may be mistaken that you won't be around when the sink hole develops. I buried the cedar stumps, but I would not bury a pine, fir, oak, walnut, sycamore, or gum stump in an area where I wanted a yard. The sink hole could develop in just a couple years, depending on the drainage characteristics of the soil.