monitor does not wake with computer

Did you disable switcheable graphics or anything like that and are you sure you were using the intel driver when you tried? Which Intel CPU do you have? Support for Skylake might be a bit screwy in 4.4/4.6. You might need to update the kernel.

Nope, don't believe I disabled switchable graphics. Yes, on Skylake. I'm using nvidia-370 and now the mentioned monitor wakes on resume but an additional monitor does not (the one usually detected as primary for greeter, though it isn't the primary on the OS). So it looks like the wake-on-resume is a driver issue so you can close this ticket. (Wish I could help diagnose graphics issues more, or at least determine if it's a driver or OS issue. There are daily graphics issues at Stack Exchange and I wish I could help, or at least help triage the right place to send bug reports...)

Actually, I take that back. Just resumed from forced suspend and only the monitor detected by Greeter as the primary monitor turned back on. (Other one had to be manually turned on.)

To clarify, the monitor listed first by my graphics card is the one treated as the primary by Greeter, and it turns on after resume from suspend. The monitor listed second by my graphics card, the one that is my actual primary within the OS, has to be turned on manually. Happy to do whatever I need to resolve this for me and other users, just need more guidance or pointed somewhere