Phrags. Elizabeth Castle, Jason Fischer, Memoria Dick Clemens, are the reddest I've seen. There is a picture of a St. Ouen 'Sangre' on the Orchidbabies LLC website that's very red. For darker Phrags, China Dragon and Sgt. Eric casn get dark. I have a lot of plants w/ these Phrags crossed in my collection. It will be interesting to see how they come up.
I have a Phrag Brecko-Nitament (Andean Fire x Nitidissimum) cross re-made by the late John Schwind. It has the deepest red mahogany color. Rich red-purple-brown that positively glows.
Generally, accept the fact that the color "red" in besseae is a thin layer of purple over a yellow background. This gives scarlet orange. Unless you knock out the yellow, you will always have some orange color in there.
The sargentianum & lindleyanum have fine purple hairs on the petals. when bred with besseae, this inherited layer of purple hair turns the color more 'red'. If you shift the yellow background to white you get either pink as in schlimii, Hanne Popow or hot purples as in St Ouen.
So true reds really don't exist in Phrags, but in some hybrids the layers of color give you a nice 'red' look. Shop plants in bloom, and then remember, culture is everything. That 'red' looking Magdalena Rose, may bloom pale red over orange and yellow if you grow it too warm, not enough light and not enough fertilizer.
Color is tricky, when good, it is great.