A Stump Grinder seems to be the Quickest, Safest, and most of all ENGINEERED to do this on a repeated basis. Yes it is an expensive piece of equipment to own, but a 2 day Weekend rental wouldn't be to bad and grinding all the stumps that have been cut previously should not be a problem.
From what I have read it sounds like you are wanting to stand over the Stump and "GRIND" the stump out with the Tip of the Blade on the Chainsaw. If this is being done on a very large stump or for a number of small stumps that is going to be very exhausting process, not to mention the Excessive wear on the chainsaw mainly from the vibrating/bouncing of the tip of the blade. And as mentioned earlier, if the saw KICKS BACK or jumps to one side( bye-bye foot) it might be nice to have a fully staffed TRAMA unit located 15 feet from the location.
If it were me, I would stick with what a chainsaw is intened for and a little safer when CROSSCUTTING Lumber. And rent a Grinder for one or more weekends.