This is some crazy level of overthinking :- ).
HDRi loaded as environment should absolutely not be loaded with tonemap control. You need the true linear unclamped values to light the scene, and these values shouldn't change between rendering restarts.
What you then visually see in Framebuffer is completely different thing. If you want different tonemapping for your environment and the rest of your image, then make a copy of your HDRi, place it into "Visible directly override" and then you can put tonemap control on it, together with CoronaColorCorrect to create your own tonemapping.
For most realistic approach, you wouldn't do that, the image and environments should tonemapped globally together in framebuffer. For creative approach, you can load absolutely anything in "Visible directly override", even tonemapped jpeg with -3 EV exposure correction to get that american look of blue sky visible from inside.
