I think those lights in HDRI are much bigger than CoronaLights in your studio. You can see it yourself, create new camera in scene center, apply CoronaCamMod and set projection mode to spherical, set image aspect ratio to 2, hide all geometry, but leave lights. Now render image and compare it to your HDRI. I'm pretty sure that rendered lights will be much smaller. You can even save render to exr, load it to enviroment and render your studio - shadows should remain exactly the same as with CoronaLights.
