Try cobalt drills and increasing your peck distance.
Stainless work hardens so every time you peck the drill has to punch through a work hardened surface, increasing the peck distance reduces the number of times it has to do this.
If the chips are coming out of the hole nicely you might be able to go to 2 or even 3 diameters.
Another thing with stainless is that just when the drill is breaking through it get very hot necause there is not much metal below the cut to act as a heat sink. Try to arrange your peck distance so you pull out a little bit before break through so the hole can fill with coolant and cool off.
An open mind is a virtue...so long as all the common sense has not leaked out.