With almost clockwork regularity someone drifts into these waters complaining of the seeming inability to print their very own concept of red.
These pleas for color guidance invariably produce others citing their secret RGB or CMYK formula for their own favorite red. They produce these color combinations as if they're disclosing a formula for turning lead into gold.
Unfortunately, any specific formula for some color or another most likely isn't transferable from one printing environment to another. A specific color composition that works for you may or may not work for someone else in different circumstances.
Reds are not difficult to produce. Custom profiles are not necessary, or even desirable in most cases**. I love to say this,m it makes the coloristas, lurching through what passes for their lives, foam at the mouth. Rather a single decent profile, proper setting of your rendering intents, and an actual understanding of your equipment and what you're doing will produce a far better red than all of the custom profiles and secret formulas extant.
The intent of a profile is to match some external environment or another to the output of a printer, not to yield good reds or good anything else.