We don't have any canon examples of how someone is turned into a blampire, do we? (Though, I'll admit that I may not have read their entry in OW well enough... Will fix that now)
You might want to read the short story "It's my birthday too".
where during the story a master Black Court Vampire creates three new vamps, implying that it takes minutes or less to make one
What about the white Court? As I see it, many of those who grow up like normal mortals should have ethics and morals like a normal mortal. So, at least for some of them becoming a mindsucking monster isn't really an option - if only they have a chance to resist. Sure, some of them try, more or less successful.But I'm sure that a competent wizard or some sponsoring source could provide further assistance, be it with tattoos or something else.
This was debated a while ago. Basically:
The Red Court Tattoos would have required lots of research to create. Think Harry as he was at the beginning of Summer Knight, but going on for years - maybe decades. It requires a wizard (or group of wizards) who really need to help a red court infected person. Probably a loved one.
It's no cure, but it's a partial treatment for someone to you have to save.
Compare "my loved one was infected by the Red Court" with knowing a young member White Court, one that hasn't transformed yet. Would someone have the year or decades required to find a treatment? Probably not, but luckily long before they came up with anything like the tattoos they would stumble over the cure. There is no cure known to mortals for Red Court Infected but there is one for White Court Virgins - and manipulating them into loving someone for that first time would be much easier than creating a treatment.
It's like the difference between diabetes and appendicitis. There is no cure for diabetes but we have developed a treatment that can keep diabetics alive and relatively healthy - but only relatively. Diabetics sometimes go blind or lose legs or encounter other health problems while insulin keeps them alive. Appendicitis isn't usually chronic - but if you don't have access to surgery it will kill you. And while it is routine surgery now it was major, life threatening surgery for decades after the invention of insulin.
The tattoos = insulin = treat something that can't be cured.
Loving your first one = operation = a drastic treatment that cures the patient.
Richard