After hours with Tech support (as helpful or as unhelpful as they could be, given this situation) and studying the many responses and attempts on this board to remedy the similar problem I faced with my 27" iMac (late 2012. 2.9 GHz Intel Core i5) after installing El Capitan, I decided to try a solution for myself: erase and the HD and start over from factory settings. Fortunately, I was able to back up all the most pertinent files I needed---most, but not all---before starting over. I gradually updated OS through to Mavericks; including all updates, and my computer is running perfectly. It's been three days, and it's running as if new: no crashes, no slow response time, no beach balls. I'm considering expanding the experiment to downloading Yosemite. But only after I can complete some work at hand.
It was very disappointing that Tech Support was unable to help; this problem seems alien to them, in spite of my forwarding this lengthy and important thread to the senior tech advisors I spoke with. Even stranger, my computer didn't qualify for a replacement HD, according to the serial number I have.
I arrived at making the decision to erase the HD partition only after many attempts to solve the issue, either through advice from Tech staff or my own research, i.e. restoring from my most recent Time Machine backup. All previous solutions (no, I was not going to bring my machine into the store only to be told what so many others were told, that there wasn't a problem, or to be sold some new temporary fix) did not work and/or worsened the problem.
If Apple were made to be as responsible to the problems their machines face as any American car company would, we'd have some answers. The late model 27" iMacs are not equipped to deal with the recent upgrades, in particular, El Capitan. A hypothesis, only, as I've still more experimentation to do. But just my two cents on this sad, frustrating issue.
