I've been using the Contrasts for about two and a half years and had great success with them, I swear by them now.
The white undercoat should be no problem. I've used spray primers varying from white, to tan, off-white, light gray and all worked well with the Contrasts.
The primary thing with undercoats is that a spray or airbrush undercoat is really what the Contrasts were designed to be used over. A brush on primer or brush on paint underneath the Contrasts is problematic because it tends to bead up on it like water. The Contrast need something to bite into so the color can take hold and kind of soak in a bit.
I don't think not shaking it enough is an issue. I've used Contrasts after shaking it but I've also used them where I forgot to shake them and they still worked just fine. Of course you do want to shake them up but I would think a few seconds of shaking is generally plenty.
It is possible as you said, that you are applying too much Contrast. I've used both Guilliman Flesh and Dark Oath Flesh and have gotten super results on faces and hands.
The thing about Dark Oath Flesh especially is that is a very strong Contrast, seems to be stronger than Guilliman.
You can spread out a very tiny amount of it over an entire face.
What I would try is to dip your brush in the Contrast so that the bristles get soaked but just barely.
Then touch the Contrast to one corner of the face and try to spread it as far as it will go. You'll be amazed how much you can "push" it into the recesses even when it seems like you don't have enough on the brush. It's always better to go back and put a bit more on the brush if you need rather than start with too much.
That's really the key. A small, small amount of Contrats will stain all the high areas of the flesh and then what's left will be pushed into the crevices and creases.
Here's some pictures of mini. I used the flesh Contrasts on. For these three dwarves I used just a small dot of Contrast on each face and then spread it out:
On this ogre, same deal. You get those nice, bright high areas and softly shaded recesses by using as little Contrast as possible and spreading it out:
This 3D printed Bilbo Baggins model is one of the largest models where I used flesh Contrast. This model is actually 100% Contrast colors. He's 54mm scale. For his face and hands I used a small brush and started by pushing Contrast into the crevives first and then using what was left on the brush to finish staining the rest of the surfaces:
One of the difficulties with the Contrasts is GW's hype about how you could just "slop it on" with a big brush and get awesome shading and highlting. Well, that's SORT of true, lol.
The problem is that certain colors are far, far stronger than others. Some of the darker browns and blacks are so strong that using them at full strength is takes a lot of practice. I tend to dilute them with Contrast medium so that they are not quite so strong.
Other colors like some of the lighter greens and yellows work spectacularly well at full strength.
Blues same deal, some of the darker blues tend to be very strong.
Some of the browns like Skeleton Horde and Aggoros Dunes are much, much lighter and weaker and can be used at full strength and give really good results.
Another issue is that the bigger the area you try to cover with Contrasts the greater the possibility of splotchiness and unevenness in color. Only way to remedy that is again to use less Contrast and be aware of any dripping and to lift it off the model with your brush before it has a chance to pool and dry in a clump. For example doing a model like a dragon or giant and using a flesh color on them is a challenge for the above reasons.
But no matter what the strength of a particular Contrast color is, it's always best to start out using as little as possible and then add more to a surface if needed.
Here's an other example of larger models where I used flesh Contrasts on the skin. This is indeed Dark Oath Flesh on these hill giants. You can see on these that the shading did come out pretty nice, but there is some splotches and some of the shading is a bit too strong. What I usually do is I add a dry brush highlight over a flesh Contrast to help soften some of the splotches. In this photo the models just have the initial coat of Dark Oath flesh, I haven't done any dry brush highlights yet: