Agreed on all of the above with the addition of LOTS of cutting oil to keep your cutting edge in as good of shape as possible for as long as possible. If the hole is so deep that you need to peck, it's trouble. If you manage to hit that magic feed/speed where it keeps a chip cutting, keep feeding don't stop!
Cutters and drill bits with a bit of cobalt in them can help. I recently had a troublesome SS bolt to drill out that was already work hardened by a friend. TiN coated endmills were building up the stainless on the cutting edge and generally performing miserably. The cobalt drill screamed, but it got through the whole job, edge intact, with a fair amount of feed pressure. I would have liked to find out what a carbide endmill did to it, but the job was done.
One big tip I recently discovered is while TiN coatings (the goldish coating) are great for avoiding aluminum buildup on the cutting edge, avoid TiN coating on troublesome stainless , because the coating causes a less sharp edge because of the thickness of the coating. I've yet to do a side by side comparison, but it sounds good to me and my uncoated cobalt bits have worked well for me. Skip the coated, and use lots of oil, and feed hard, and spin slower.