You do have to cut the roots from different angles. Its easier if the stump is NOT cut flush to the ground so you can grab it like a loose tooth-tell the tree guys to leave a foot or so.
As far as nice lawns go, you're talking about a 7800 lb, 6 foot wide machine that turns by ripping up the ground-maybe not the best residential stump grinding tool. I see a lot of plywood in your future. Better stock up on sprinkler heads, too.
You've already got the S250 and want to make it work-I get that. Lot clearing, site prep, storm clean up, and front yard stumps can still be done. I just think, for all around versatility, its really tough to beat a little Rayco. I'd look for a good used 1625, 1631 or 1635 to compliment your S250.