11-Month Old Still Doesn't Sleep Through the Night

I feel like I've been writing a lot lately, but the advice has been good, so please help me out again!

My son is 11-months old and sleeps through the night only 3 days a week on average. He has a bedtime routine and puts himself to sleep beautifully for his nap and every single night - I haven't rocked him to sleep since he was probably 8-months old. But about 4 nights a week, he wakes up sometime between 12 and 4, and stays up AT LEAST 2 hours, crying and screaming the whole time. He is not having nightmares (he does occasionally have nightmares, and his behavior is very different on those nights).

He will take a bottle, but only a couple of ounces, and it in no way helps him go back to sleep, so I stopped giving it to him. He also eats a big dinner and takes a bottle before bed, so I truly don't think he's hungry. He does NOT want to be rocked, and will squirm and fuss if I try. I even tried bringing him into bed with me (in desperation), and he didn't want that, either. What he does want is to get down and play. If I let him, he will stop crying and will play on his own for about an hour to an hour and a half, and then tell me he is tired and want to go back to sleep. In the beginning, I let him do this a couple of times, but I began thinking that he was waking up more often (in the hopes of getting to play), and so I stopped doing it. I changed his bedtime and his wake-up time, but it had no effect on how often he woke up.

So for the last two months, I've been letting him cry it out, basically, since nothing else has worked. I let him cry it out when I was teaching him to put himself to sleep, and it worked really well. On these nights, I go in and give him his paci, and then leave again and try to get some sleep. If he screams, I will go back in to check on him and make sure he still has his paci (he usually does). I get a little more sleep this way, and he does eventually put himself back to sleep, but it often takes 2-3 hours, and after two months of being very consistent with this, he still wakes up more days than not (so I'm not really seeing too much improvement in his schedule).

Does anyone have any new ideas about how to reduce the number of nights he is awake? My doctor suggested the CIO schedule above when I told her about my problem, but like I said, although I am getting a bit more sleep that way, he actually is not. The next morning after he has been up, he is always exhausted and cranky, and wanting to take his nap several hours early. I don't have a doctor's appointment for another month, and in the meantime, we're both exhausted. Help!