Ok. I think it seems to be fixed in 16.9.1.
While i was looking through the release notes of the various hotfixes, I spotted this 'known issue'
"Shader Cache may remain be enabled when set to "off" in Radeon Settings on some Hybrid Graphics configurations."
for all drivers between 16.7.3 and 16.9.1 hotfix. 16.9.1 itself *didn't* list this, either as a 'known issue' are that it was fixing it.
Since the graphics problem seemed to be a shader issue of some kind, I tried turning the shader settings off in AMD settings. no effect, but since it was a 'known issue' for the later hotfixes, i assumed it was probably a problem with 16.7.3 as well. I tried upgrading to 16.9.1 to test switching the setting on and off (and to the default 'AMD Optimized') and the problem didn't come back. So I guess 16.9.1 fixes it? Odd that it doesn't say anything about the fix (that I can tell) but maybe it was incidentally fixed with some other issue.
Either way, i'm not complaining. Thanks for that help, Fred_vdp. And graahf, hopefully this also works for you.
EDIT: wrong version number.
TL;DR:
Recommended steps (from my perspective):
download both 16.7.3 and the 16.9.1 hotfix here. http://support.amd.com/en-us/download/desktop?os=Windows+7+-+64
uninstall old drivers
restart
clean install of 16.7.3,
restart,
then install 16.9.1 hotfix
restart
run DA:I. enjoy (hopefully)