This paper employs direct spectral fitting of individual orbital data in order to measure rapid X-ray iron Kα line and continuum spectral slope variations in Seyfert 1 galaxies with unprecedented temporal resolution. Application of this technique to a long RXTE observation of MCG -6-30-15 indicates that the line flux does vary on short (1 day) timescales, but that these variations are not correlated with changes in the continuum flux or slope. These rapid variations indicate that the line does indeed originate close to the black hole, confirming predictions based on its very broad profile. However, the lack of a correlation with the continuum presents problems for models in which the line variations are driven by those in the continuum, modified only by light-travel time effects. Instead, it may be that the line responds according to a physical process with a different timescale, such as ionization instabilities in the disk, or perhaps that the geometry and physical picture is more complex than implied by the simplest disk-corona models. These data also indicate that the slope of the underlying power-law continuum (Γ) shows strong variability and is tightly correlated with the continuum flux in the sense that the spectrum steepens as the source brightens. All of these results have been checked with extensive simulations, which also indicated that a spurious correlation between Γ and Compton reflection fraction (R) will result if these quantities are measured from the same spectra. This casts serious doubts on previous claims of such a Γ-R correlation.