i break all the long roots off and dig a hole in the same place about 6 foot deep and bury the stump
When the stump rots will you not have to fill in the area where the ground sinks?
I do what Eddie said, just dig around the stump, when you hit a root you cant break with the hoe did out from the stump until you can break the root. Then you can use the hoe to break that root closer to the base of the stump. You need a dig a real big hole for a real big stump.
I usually start by digging a trench down one side of the stump, about 2-3 foot away from it. Dig it about 6-7' deep, you'll break quite a couple roots this way, again just dig out until you can break off the roots. If you position the bucket so the teeth are under the root, then use the curl to break the root.
Pile the dirt as far away as you can, its annoying having to move dirt away from the hole.
Once youve got the trench try diggin in closer to the stump along the line of the trench.
Do this on all sides of the stump. if you uncurl your bucket all the way you can sometimes scrape under the stump a little. Also if you drive you you are right up close the stump, and dig on the other side of it, so you can dig under the stump (you cant see what you are doing this way, just have to guess whats going on).
Eventually the stump will the standing on an island in the middle of a big hole, and you can use the hoe to break it off and drag it out the hole. The stump might break out at any point before that depending on how easy the stump is, you may get away with digging only 2 or 3 sides.
Just keep at it. I've had some large pines take me a whole day, but I used equipment smaller than yours.
The pic below is of a 18" diameter pine, boy did it have alot of roots, and it was a mighty big hole, about 6-7' deep, and 10' square. 1/2 day job.