My tact has been to dig to China all the way around the roots. I use a very sharp polished axe to whack at the 'unbreakable' roots. Goes through them like butter. I've had pretty poor luck with the sawz-all option...even with the long blade, any dirt that gets in the cut chews it up in a second to where you're sawing with nubs. If you are VERY careful about dirt, maybe, but I haven't had many holes without dirt!!! And no, I don't risk my chainsaw blade. Did it once. The fun lasted, literally, about 4 seconds.
For Pines: You can dig closer to the stump and just KEEP DIGGING. Eventually, you get below the tap-root and the whole root ball just tips over. Flip it in the hole and knock the dirt off, then lift it straight out.
For Oaks and Maples, you need to get a little further out. These, you can 'pry' up with the boom on float and using the back of the bucket for leverage. They pop up like a soda cap. Flip it over, knock the dirt up, and drop it in your trailer.
I've removed 8 or 9 Pine stumps to ~15" diameter and several Oak/Maple sumps, some of which were split-trunk monsters. Oddly, the most difficult was a smallish (~8") pine that just wouldn't let go. I had to go over 4 feet straight down on all sides before it would finally give way to the bucket...it was just flopping around the hole for a solid 30 minutes while I kept digging to liberate it. Very frustrating.
Typical dig/remove and replace soil takes about 1 to 1.5 hours.