Two possibilities: Pre-compose everything and fade the comp or use a second layer that has the layer styles, but in its Blending Options for the layer styles has set Fill opacity to zero, so only the styles are rendered, but not the source. Whjat you are seeing is normal behavior based on how styles are supposed to work. Whenever there is a non-zero (non-transparent) pixel, the get applied, where the pixels opacity acts as amultiplier for the style's intensity. Looks good for some, but often causes this popping appearance...
I think that the only thing causing you problems is the stroke. Try adding the stroke using the character palette instead of layer styles. Now if you simply add an opacity animator to the text layer, set the opacity to 0, and animate the Range Selector you should have what you want.
Thanks Rick. That works. Using the character pallette to add the stroke, however, curiously gives a slightly different look to the letters than when applyng the stroke as a style. But at least the stroke color doesn't fade up first. Thanks again.