You think it's the screen/hdmi at fault, but it might not be. I've had the problem with two laptops in the past (the bug was with all distros I tried), and in one case it was a BIOS that Linux didn't like, and the second one was the internal wifi that its linux driver was buggy. For the first laptop there was nothing to be done, so I disabled sleep completely in the bios, while for the second one, I disabled the wifi modules in the kernel's blacklist, and then used a usb wifi that I knew it worked better. Both cases were appearing as a dead screen, but it wasn't the screen/hdmi/gfx card to blame. In yet another case, with a thinkpad laptop, the wake up was working, but it would wake up 30 seconds later than anticipated. In that case, it was the fact that its thunderbolt was dead (hardware had gone bad), and only when I disabled it in the bios completely the laptop would wake up correctly and fast.
In all those cases, I had to look at the kernel logs to see what was the issue. There were traces of the problem of which hardware exactly was creating the problem. It might look like a screen/hdmi problem, but most of the times, it's not.