I would say intuitive minus a few cases that just suck to figure out something optimal/ do-able for.
Anthony Brooks (The Westonian) has a pretty sweet video going over a few of those cases.
http://www.youtube.com/watch?v=ltRk3QjGtmg&feature=channel
Some of them are pretty obvious, others notsomuch but still hope it helps.
Take F2L very slow make sure you get all of your solutions under your fingers. The biggest thing to remember is that wi an intuitive aapproach you are creating your own algs. All 42 cases can be broken down into the basic 3 and your job is to figure out which of them makes the most amount of sense for the situation your in, avoiding awkward cube rotations and extra moves for example as the F2L is all about efficiency.
Take this case for example and assume no open slots: You could set it up so that white was on top and solve it that way (R U2 R' U2 Y L' U2 L U' L' U L) A fine solution but there is a cube rotation and its a little long. you could rotate first and solve it as follows: (Y L' U L U' L' U2 L U2 L' U L) solving with the rotation in front doesn't inturupt the flow of the actual alg itself which is great as it helps with consistancy however it is rather long. Comparitively if we think about it there is a way to make this case very very simple using a double layer turn (d in this case) the alg then becomes very simple and aviods a left hand exicution which most beginning cubers find difficult, I know I did and in some cases still do. So with the d move the alg is as follows : (d R' U R U' R' U' R) This alg is 8 moves as opposed to the other two which are 12 moves long. It is these sort of inventive solutions that an intuitive approach allows, with a pure alg you hsve to set the correct possition then exicute, which takes valuable seconds. Though in most cases this is a much more difficult approach once you find something that works you can really can reap the benifits.
Each of the cubers you mentioned are intuitive solvers, I know that Feliks knows some ZBF2L but it isn't his bread and butter so to speak. I can't say if the others use ZBF2L but i'm sure they know a few cases here and there.