I just went and found the mushroom again to smell it, and I was still unable to detect anything. I don’t have the best sense of smell, but this observation matches the text in my Miller guide – “Odor not distinctive”. The other Hygrophorus species that book lists are also mentioned as being odorless.

isn’t always distinctive, and maybe not sensed by everybody. I find it often rather subtle.

She mentions no distinctive smell, the book I’m looking at mentions a distinctive odor of sage!

Yes, this looks like the one you call Hygrophorus eburneus. I don’t know which one you actually have in California.
In Europe, we are now regarding Hygrophorus eburneus as a species growing with beech, the similar Hygrophorus cossus with oak. They can also be told apart by a KOH reaction on the stem base (brownish orange on eburneus, none on cossus).

Here is a nice observation of that species from CureCat showing the slime!
http://mushroomobserver.org/30932?search_seq=1200637