You tried SAVI? What L-factor did you use? Did you try the modified version of SAVI? In an area like Bryce Canyon you will have a huge soil brightness component. I highly doubt that L=0.5 would adequately account for the soil line. You can empirically derive the L factor by plotting the red and nir bands and defining s by identifying the slope where vegetation drops out. Then L is derived by:
L = 1 - (2 * s * (nir - red) * (nir -s + red)) / (nir + red)
The MSAVI is a bit more robust than SAVI and is derived, using the L factor, following:
MSAVI = ( (nir - red)(1 + L) ) / (nir + red + L)
Qi et al (1994) solved for a range of L and came up with a derivation of the modified SAVI that avoids having to derive L explicitly. The SAVI2 formula follows:
(2 * nir + 1 - sqrt((2 * nir + 1)^2 - 8 * (nir - red))) / 2
Another alternative is the SATIV or total vegetation index (Marsett et al., 2006). This metric is more akin to a measure of fractional cover. The SWIR2 (2.09 – 2.35 nm) band is used in addition the red and nir, the metric derived following:
SATIV = (nir - red) * (nir + red + L) * (1 + L) - (SWIR2 / 2)
I would highly recommend standardizing, whatever metric you choose, across your time series. This could be done via a row standardization or following methods in Peters et al., (2002).
Marsett, R.C., Qi, J., Heilman, P., Biedenbender, S.H., Watson, M.C., Amer, S., Weltz, M., Goodrich, D., Marsett, R. 2006. Remote sensing for grassland management in the arid southwest. Rangeland Ecology and Management 59:530-540.
Peters, A.J., E.A. WalterShea, L. JI, A. Vliia, M. Hayes, M.D. Svoboda (2002) Drought Monitoring with NDVI-Based Standardized Vegetation Index Photogrammetric Engineering & Remote Sensing 68(1):71-75
Qi J., Chehbouni A., Huete A.R., Kerr Y.H., 1994. Modified Soil Adjusted Vegetation Index (MSAVI). Remote Sensing of Environment 48:119-126.