Drilling 304SS is a walk in the park. I routinely run a job using a #10 (0.1935") drill in 304 using a Guhring GT100 high speed cobalt drill. I think the problem you are having isn't the drill, it's the SFM. My Guhring book calls out, for the drill I am running, 25 SFM and 0.002" IPR. I have been successful getting this drill up to about 45 SFM without any adverse effects, leaving the feed at 0.002" IPR. I am only going 0.900" deep, but I am using the 0.200" peck you are. I have been using the same drill now, without sharpening, for about the last 1500 parts and it's starting to look like it is going to need to be replaced.
If you have a large run of parts, and the job warrants it, and you have HP coolant, I would give the folks at Mitsubishi a call. Their drills are pricey, I'll give you that, but I have found no better carbide drill and certainly no better customer service in my area than them. Second to none in the Northern Michigan area! I use their MWS drills in 303, 304, and 316 all the time. Come to think of it, there is one running right now. 0.319" Diameter, drilling 1.300" deep, 2500 RPM, 0.006" IPR, no peck in 303SS.
Sorry for babbling. Just lower the speed with your cobalt drill and you should be good to go.