I installed SMS popup app (it's free) and then tweaked the settings of both
default message app settings
as follows to get the behavior I wanted.
I think that you could get any of the behaviors that everyone is asking
for through the combination of settings.
Basically you have to turn off the popup for text message in the default app
since SMS will also popup, so you have 2 popups happening. So just turn
off the default message app popups.
The you can control the screen coming on or not for sms arriving through
SMS popup.
default message app settings
SMS popup settings