While the zoom combo you have is incredibly versatile, both lenses are quite large & heavy.
That being said, if you were to replace those two with all 5 of those lenses you're interested in, you're not saving any weight, and you have to swap lenses all the time, or decide what to bring and what to leave behind.
In my opinion, the 24-70 can in many ways be replaced by a 35L, I've done this, as have many others, but the 24-70 is still an excellent lens (It's popular for a good reason).
The 70-200 for me has been replaced by a 135L. I lose some versatility on the shorter end, but there's only been a handful of times I've not been able to backup enough to get the framing I want.
If you were to then ad something wider than the 35, you'd be pretty well set.
I agree with most of what you've stated here, I don't worry about the weight of the lenses in my bag, as I have a roller to carry around, or roll around, so really the only thing on my neck is the lens and body. Which the 35L is a LOT lighter than this 24-70, for sure. I do have to switch, but I like how hit makes me think. Not sure I want anymore zooms, I'm almost certain I'm going to go all prime.