I think that we have two separate problems here.
1. Failure to wake up from sleep
On my iMac, I've encountered the same problem with a separate 27in LG high res monitor. The only cure that I've come up with is to change the energy saver settings in the Preferences to 45 minutes. Not exactly environmentally friendly, but something has happened here with the system software, since this was not a problem in prior OS releases.
2. No signal or corrupted signal to the external monitor
The existing iMac was a replacement for an older 2009 Intel Core 2 Duo iMac, which mysteriously lost the ability to display anything on the external monitor after a system upgrade. I discovered that Apple apparently dropped support for the video card after 10.7. After serious time troubleshooting this, including trying the external monitor with a similar vintage 24in iMac where it did work, there was no other conclusion to come to. I'd suggest anyone encountering problems with external monitors with iMacs or any Mac laptop to try the monitor with another machine or with something of newer construction. That may provide your answer. It will not fix the problem, but will let you find out if your video card was one of many that Apple chose to drop support for.
With the other issues that many posting here have indicated, I don't think that Apple's quality control or their support for their product is what it used to be five or six years ago.
FWIW,
L Cranston