Try painting the under-layer with an opaque earth red such as indian red or venetian red. You can then use your regular colors over it. You might even find you don't require the extra punch that cadmiums offer.
Alizarin and perm rose are very transparent pigments and so is your medium containing varnish. I don't know if there is a brand that can overcompensate for those choices. I use Michael Harding paints which I feel are far superior to any other brand I've tried.
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