I would like to tell you about AE-L, that is, auto-exposure lock. This feature enables you to lock the exposure reading in the specific and does not change when you re-compose the shot. The exposure reading remains the same despite the change in the level of light.
I learned about this technique while researching on various exposure modes of the camera. But have not got chance to put it to test yet. But I think this can help you in getting the exposure you want.
Please do try it out. I would love to know if it helps.