If all else fails, cheat!
So the basic problem is if the HDRI background outside is bright enough to light up the interior, its image in the windows get washed out? And if you reduce its intensity to avoid that, the inside gets too dim?
Then why not selectively use two different intensities? Namely, a bright one for indirect rays, and a dimmer one for camera rays? Then you get to have it both ways. 
Here is an example of what I mean by selecting between two different intensities, based on whether the ray is a camera ray or not:
And here is what the inside of the “Select” node group looks like:
