Most paints art not opaque painted thinly especially in one layer. Ditch the mediums, they are deleterious and just use a thinner to get the paint to the consistency you want.
Alizarin is one of the most transparent colors there are. Do not mix white to make any red opaque. It will only dull it. If you need to lighten a red up add some genuine Naples yellow.
A very opaque, albeit pricey red, that is the most opaque I have ever used is the Vermilion red by Michael Harding, It is $50 a tube and well worth it .It is sold by the Italian Art Store,
www.italianartstore.com. He also makes a genuine Naples yellow. The light one is the one you want. All the other manufacturers make a mix of a cadmium and white. It is not the real thing.