I put 3 tons/acre on my main plot a couple of years ago and I didn't even have a soil test to justify it. I knew it had been at the very least 5 years, and probably a lot longer than that, since it had been limed. As Mike said, 2 tons/acre is the normal rate farmers routinely spread lime anyway. Since it's so hard to get somebody to bring a truck for a small area, I got the fella to put a full load on my 4+ acre plot when he was able to get to me.
Since you did put the full rate on your plot you should get good results if the rain will cooperate.