We have increasingly been being exposed
While this may be technically correct ("been being" is jarring), what you'll hear/read more usually is this:
We have increasingly been exposed
This means that "over some time period in the past, we have been increasingly exposed", and that the increasing exposure may or may not be continuing now - but the strong default assumption would be that it is continuing now, since if you said
We were increasingly exposed
this would mean "we aren't being increasingly exposed" anymore.
We are increasingly being exposed
This means that now, we are being increasingly exposed, whereas before now, we were not being increasingly exposed. (Previously, we may have been simply exposed, but not increasingly so).