This is possible with Popup Blocker--but that tweak hasn't been updated for 6+ yet, and when I contacted the dev over the weekend, he had no ETA. Said he hasn't had time to look at it yet.
I did try it out before I emailed him, as it's one of the tweaks I normally depend on. Several functions *did* seem to work, but closing a notification with the home button crashed the phone immediately into safe mode.
Hopefully someone has an alternative, as I'd also like to keep the screen from waking on some things, but need to be able to exclude other apps from that function.