The 1200 UTC sounding suggests that the strength of the inversion should be weakening thanks to this morning's precipitation.
Although we were saturated at the surface, it was quite dry in the 850-700 mb layer. Assuming the rain produced sufficient evaporative cooling to bring the temperature to the wet bulb (blue line), temperatures in this layer would be about 3-6C colder. Unfortunately, that's not enough to mix out the lens of cold air in the valley floor, but it might allow for some stirring along the benches. Some evidence that this is occuring is provided by CO2 observations from Sugarhouse, which did not peak as high this morning as previous days.
Later today, cold-advection drops 700-mb temperatures to about -7C. That will help further, but it is not enough to mix out the valley floor thermodynamically (based on a dry-adiabatic lapse rate). Will that lens of cold air near the valley floor remain? This is certainly going to be an interesting case for PCAPS.