OK, coming into this thread probably two weeks too late, but just in case anyone's still interested...
Kuzushi is vital to 'proper' judo. The example given for kata guruma is quite right, and that's more or less how I'd expect to apply it against an untrained opponent. Unfortunately, even just in randori most times your uke isn't going to give you the kind of momentum you need to apply technique in the classical sense. So you need to create it for yourself.
One tech that the instructors at my school (many of whom are of the big, strong variety) use on me a lot is to reel me in until I am locked up against their torsos with their centre of gravity below mine, then move us both as a unit until I am off balance, and WHAM! Myself, I don't like that approach all that much, but probably just because I can't do it right.
That's one way, but there's lots of others. These include things like lifting or drawing back your grip, stepping so as to make uke step with you, or stepping into uke so you occupy his base. The most important one, however, is probably combination attacks - forcing uke to react to one or a series of attacks until you feel that he is off balance, then throwing him accordingly.
Digging into my old yellow belt curriculum for a specific example here. Hiza guruma is a good example of a throw where you get kuzushi by stepping and using your grip. Assuming you start with a right grip, the first stage is to take a left step forward. This should force him to take a right step back. Stage 2 is to give him a light tug to his right front corner. So he feels a pressure backwards, then a pressure up and forwards. This should ideally force him to take an off-balance step forward with his right foot. Stage 3, as you feel his balance go, you place the sole of your left foot against his right knee while giving a quick twist to your left and pulling out and down. The forward motion of his leg should stop against your foot while his torso keeps going, and he should roll over his knee. Works great against the stiff-arm tpes.
I think you've said in the past that your school is pretty hard on the tests. However, I think when I did my yellow, while I had to know what kuzushi was, nobody was particularly looking to see it applied all that well. I think if you can just demo the techniques in the curriculum with a reasonable degree of understanding you should be fine.
Cheers,
JG