OK, so we won't harrass you about obviously building without a permit, which would have required proper footings!
I believe you could excavate under the post location without too much difficulty. The proper footing probably needs to be 12" X 12" X 12" deep. This could be dug fairly easily, then with a form on the outer side with just room to get the concrete in. The new form could be kept at or below ground level, so it would not look bad.
NOTE: You probably would want to intstall a temporary ledger with jack studs at each post as you do them, one at a time, so that the slab portion you are digging under is not taking the post load until the new footer has set up.