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I'm having trouble deciding on a portrait lens.
Be very careful to think and define what you mean, but also be careful about overthinking. If you are looking for a head and shoulders portrait lens, that is rather well defined. But "portrait lens" is anything from 24 mm to 300 mm and even those limits are exceeded in a few cases. That is because portraits are anything from a full-length figure at the side of a frame to a tight crop in on just eyes.
Note also that beauty / glamour work benefits from distances about 50% greater than regular portrait work and thus the focal lengths used for the same angle of view are about 50% greater.
Just what are you looking for?
To get a perspective that gives you a "friendly" sense of intimacy you need a distance that makes the 85 mm the classic focal length on full-frame for head and shoulders. 70 or 100 mm is similar enough that if you like those lenses, don't worry about it. Maintain that distance but vary the focal length to get different croppings (like three-quarter length portrait or a head-only photo).
Regarding f/2.8, once again, you need to define what you mean by "portrait". Do you mean casual candid snaps without flash? Then get a fast focusing fast lens. If you mean well-executed intimate portraits suitable for printing large (11x14 for example), then you have time to use a tripod or to setup good lighting (turning on room lights and/or using window light) or to use flash even if it is only strategic bounce flash.
With forethought and practice, you can coax a subject into a pleasing pose and expression that can look every bit as candid as a snap and have much better lighting.
Don't overthink the lens: Get something you like, regardless of what other people say. Do think deeply about lighting and posing and rapport.
With regard to specifics, the 24-70 II and 50 L are great lenses, as you say. That you would be "underwhelmed" by the 85 1.8 is perhaps over-stated, but your lenses are in a class that you can afford the 85 1.2 if you like.
If your primary purpose is baby pictures of your 22 month old daughter, then I would look very deeply into your aversion against zoom lenses (what the heck are you doing with a 24-70 then?) and "big heavy lenses" so you can consider the 70-200 L lenses with IS and be fair to yourself.
When people complain about "big heavy lenses" of the 70-200 f/2.8 type, I say to myself, yeah, "heavier" but "deal with it". If quality photography were easy everyone could do it. (Think carefully about what goal you are really reaching for.) The weight of a 70-200 f/2.8 is really not much of a barrier to 99% of people when you think objectively about it. Yes, we would like it to weigh like a 40 mm f/2.8, but it's a lens (plus camera) and not as heavy as a weed-eater or chain saw that people use all day long.
The 70-200 f/4 IS is very good and lighter and the IS is very good for indoors. It in combination with ISO 1250 or 2000 on the 5D3 will give you excellent results. In your situation that is what I would get or splurge on the 2.8 IS II.
Regarding f/2.8 or f/4 or f/2 for indoor lighting (presumably meaning dim 100 watt incandescent lighting): I used to shoot 35mm film for 8x10s at ISO 400 (ASA 400) at f/2 and 1/30 sec carefully. These days ISO 1600 is so good on the 5D3 you can shoot carefully at f/2.8 and 1/60 in dim light and make gorgeous 16x24 prints (twice as large linearly with the same amount of camera motion blur). You can shoot at ISO 2500 and f/3.5 and 1/80 with a little less care and still make stunning 11 x 17 inch prints. With IS you can do even more.
One of the keys is to compose so that the shadow detail is unimportant and then make them darker in post-processing. Compose for the light.
In the final analysis, I think you should get the 100 mm f/2. Read what you wrote about it: you like it and can afford it. Get it and up your game in other areas.