I've discovered some fine and old documents on the eggtempera.com site, volumes of articles from the Society of Painters in Tempera.
Quoting from a portion of the article Yolk Of Egg Tempera by R. Spencer Stanhope, April 23, 1903 :
"The Advantages are as follows :-
Pictures painted with the Yolk of Egg possess the Richness and depth of Oil
Paintings, without losing any of the brilliance of colour which oil to a certain extent injures. In fact there is no medium of any kind in ordinary use for painting which so little, if at all, affects the colours with which it is mixed, whilst it gives a softness of effect which is more or less wanting in all the others; and that this quality is permanent may be seen in any Cinquecento work which has not been meddled with in any way, and the colours will there appear as brilliant as on the day they were painted. As the colour dries in a minute or two the part on which the painter is at work can be completed off-hand, the colour remaining permanently the same. The slight yellow tint caused by the yolk disappears entirely in a few days. All marks of the brush pass away as the colour dries, and a perfectness of surface is obtained without any effort on the part of the painter; and, as I mentioned before, owing to the natural grease in the yolk of egg the soft rich effect of oil is produced whilst the painting can be seen in any light as is the case with fresco or water-colour. From the day of painting the colour the surface steadily hardens and, provided the technical part of the work is properly done, this hardening process goes on without any cracking or shrinking of the surface till it reaches that pitch of hardness which is so notable in Cinquecento work. Finally, as the painter puts the colours on the panel he can judge of the permanent effect, which is not the case with mediums such as Oil, Fresco and ordinary Distemper."
I'm working on my corn but it's a slow haul. I'm checking out synthetic pigments by Kremer--rich colors and small particle size. For instance, using a cadmium yellow was an incredibly smooth painting experience but I am leaning away from toxic materials. There seems to be a good selection of innocuous and luscious synthetics.