As someone who just did the exact opposite (sort of), I would really ask yourself if this is the best course. I sold my 35 1.4, 50 1.2, and 135 2 to get a 300 2.8 II. I kept my 24 1.4 II, and 85 1.2 II, but found myself using the other lenses less and less after upgrading to the 24-70 II and 70-200 II.
If I were you, I'd consider trading the 70-200 II (a huge lens) for the 85 1.2 II and 135 2 to get the portability you desire. That's how I'd start. The 85 1.2 II is amazing and the 70-200 can't touch the look you get from f1.2-2.
If you're still having prime lust, I'd keep the 24-70 II as it's not that huge, and then pick your most used prime focal length (i.e, 24, 35, or 50) and buy that lens. For me, my love is the 24mm perspective, so that's what I kept, but others prefer the 35 or 50.
If you don't shoot the vast majority of your shots at f/2.8 or need portability, I'd just start with one prime before selling your zooms to make sure. The convenience you give up is much bigger than you think unless you mostly shoot portraits, street photos or the like.
Your last option is to rent one more primes for a week or two and try to shoot everyday with them so see if it's worth it for you. Everyone is different and I never imagined I'd part with my primes, but not that I only have 2 of them, I don't miss the rest.