It seems weight is importance factor for you. The f/4 IS is no doubt much lighter.
Do you use a strap system like a BlackRapid or something like that. Using something like a strap system or a Spyder holster system might make the f/2.8L IS II manageable for 4 - 6 hour sessions.
One major reason to have the 2.8 is to stop action, especially indoors. You don't have a need for that it seems.
How big is your studio? If it is pretty large, you might be able to make use of the 70-300mm L IS, which at 300mm will blow out your backgrounds nicely! So, if you don't need f/2.8 to stop action and you want a lighter lens, perhaps the 70-300mm L IS is a good middle ground. It can also be used as a travel lens with your 24-105mm IS.
Depends also on your style...do you want parts of their face out of focus? Then the 2.8 is needed.
In a studio, you can move around no? What do you need that your 24-105mm f/4L IS cannot give you now? I am thinkin 105mm in a studio setting as long enough. If it is shallow depth of field you are after, you might be better served by a 50mm prime: Canon 50mm f/1.2L or Sigma 50mm f/1.4 Art. Just my two cents.
Indoor sports on monopod... great... I don't care about that
I shoot mostly hand held and portrait orientation, meaning I have to hold camera body and the lens for 3-6 hours a day in this position.