Wildie, this is exactly my problem but I do not understand how you did it.
I dug down to the 4' level using a shovel and clam style post hole digger!
Under-mining the existing foundation in such a manner that the pocket for the 16" square footing was centered under the foundation.
I then filled this pocket was cement to a depth of 6" and let it setup!
Then I cut a Sono tube down the middle,lengthwise leaving enough of the tube to slip under the corner of the foundation.
Then I back-filled the hole to keep the tube in place.
Then made a sloppy mix and filled the tube up, tamping all the while, making sure that it flowed under the the old foundation.
I pushed some 3/8" re-bar down into the mix to reinforce the pier.