I've had both 15 and 17 inch 2011 models, both of which I upgraded to SSD and 16GB RAM. I have not encountered your problem. I suggest you look in System Preferences at your Energy Saver settings. I have Put Harddisks to Sleep checked, even though I don't think that is relevant to SSDs. Also, maybe Wake for Wi-Fi could be your problem. I think the Power Nap options won't be available for a 2011 model, but you would want to disable that if possible. I've run Mavericks on the 15" and El Capitan on the 17", with latest updates. Unfortunately my 15" suffered a dead logic board about 6 weeks ago, and was no longer worth fixing with the 2011 models going into unsupported status as of 2017 - no more Apple warrantied parts available. I'm not sure if the 15" died because of the known problems with the 2011 logic boards, or if it was other rough treatment that did it in - a lot of dust and dirt inside it. The 17" has had no problems after years of heavy daily use, but it has been mostly sitting on a clean desk without much carrying around.
Also, look at
Battery drain after SSD upgrade , although you say your battery drain is happening during sleep. I suggest upgrading to El Capitan, and also I have enabled TRIM for my SSDs.