The whole, any bodily fluid will do thing is kinda dumb. If any bodily fluid really will do, and the type doesn’t affect the taste for the vampire, why do they use blood packs? Blood takes a long time to regenerate and is expensive… just have people spit into a jar and give that to the vampires.
I get that the whole any bodily fluid thing is a plot point to force cheating, but… stupid problems get stupid solutions.