Unfortunately, the current shiny shader works by darkening surfaces. The new one in the windlight viewer is a little better, but it still makes white surfaces look silvery. A white gloss is not really possible.
You're on the right track by tying to fake the shine with gradients, but even that is going to be more difficult to pull off convincingly than it seems like it should be. The problem is that in real life, we have a whole lot more range of colors than we have in the computer. In RL, a white surface, no matter how clean and bright, will never be as bright as the ambient light around it. So of course there's always room for glossy highlights to make the surface even brighter.
In the computer though, "white" is a fixed value. It's the maximum sum of all colors. Nothing can ever be brighter than the color white, so of course there's no way to get a white surface to "shine". The solution, therefore, is to start with something dimmer than white, to leave enough room that the white itself can constitute the highlights of the shine. This is (in part) why the shiny shader makes white surfaces look silver instead of white.
What I'd suggest is instead of making your cabinets actually white, you use an off white, either a light gray, or maybe a cream color, as your base. Then you'll have enough overhead to go in and paint white highlights in order to make the surfaces appear shiny.
Take a look at this photo of a glossy white cabinet door knob, for example:

At first glance we accept it as "white" because that's how we're used to seeing shiny white surfaces on screen. However, run over it with the eyedropper in Photoshop, and you can see quite easily that there's almost no pure white to be found anywhere on the knob. A couple of the specular highlights have pure white in the center, but that's it.
In fact, it's usually not a good idea to use pure white, even for concentrated highlights, because it has the effect of making things look overblown. You're much better off keeping the whole thing in the slightly off white range.
Also, gradients alone won't be enough if you want it to look totally realistic. Glossy surfaces do appear to grade, but just as importantly, they have fairly extreme specular highlights, which follow the contours of the 3D shape. Make sure you paint those in, or your stuff will look flat.