What is the best current understanding of how yeast transformation works?
I have never worked much with yeast, but I can still give some answers:

Salmon sperm is used as a the so called "carrier DNA". It is thought to bind to the yeast cell wall and thus prevents that the DNA which shall be transformed does so. This raises the transformation efficiency. See here for more details: "Transformation of yeast by lithium acetate/single-stranded carrier DNA/polyethylene glycol method.".

Effect of the recovery time: In this time you typically give the cells the chance to recover from the relative rude treatment and to express the resistance gene (when used) before moving them to a selective medium. This raises the efficiency of the transformation.

Spheroblasts: As far as I remember they are terribly fragile and painful to handle. However, when you succeed making them, you have cells which take up high quantitaties of DNA which makes them pretty efficient.

I think these reviews are definitely worth looking at (they also contain a lot more references):


Genetic Transformation of Yeast
Transformation of Saccharomyces cerevisiae and other fungi - Methods
and possible underlying mechanism
Foreign gene expression in yeast: a review


If you have a chance to get hands on a copy of "Methods in Yeast Genetics: A Cold Spring Harbor Laboratory Course Manual", I think this will be very helpful.