Not sure that curing is not too different from brining. The key is to submerge the beef in the curing brine and when it reaches equilibrium it wont soak up any more. I go 7 days in the frig.
Sometimes that's the case, but brines vary in strength. The meat will reach equilibrium, but a weaker brine might not have enough salt in it to properly cure the meat. Most are strong enough, though.
Brad - most recipes I follow go by the pound for curing time, too, so the thinner pieces take much less time to cure. You could probably get away with those round steaks, but I've tried this myself (a "beef bacon" experiment) and I found that I have to watch the curing time and cooking temperature. I often use smaller pieces of salmon too when I'm curing and smoking that, and it takes a bit of babysitting sometimes or it can turn into salmon jerky (which I don't mind either).
Come to think of it, with round steak another option is to "jerky slice" the meat, and use it for making jerky, if you're so inclined (I am). Oddly enough I've never seen a "corned beef" jerky marinade in the stores, so naturally I'll have to experiment soon...