@D B Holtz - if you like the consistency of the Dr. Ph. Martin's Bombay India inks, they have a "Crimson" that is darker than their "Red."
I don't love India ink for calligraphy though (but it's great for drawing), so when I want a particular color, I use one of the Kuretake gansai tambi colors. They're Japanese watercolors - the pigments are ground a little smaller than the pigment in gouache, so they're a bit silkier, but bigger than watercolors, so they're opaque, and they don't bleed on most paper. And they have a resin binder, so they dry with a bit of a gloss. The box sets include a variety of reds (cools and warms, brights and rich tones) as well as other great colors. And of course, you can mix them to make any shade you like. They come in dry pans, so you mix them with water to whatever consistency you like, and then paint them onto your nib, just like gouache or like an ink stick or like the Coliro/Finetec colors/shimmers.
Otherwise, Diamine has some nice reds - "Matador" (fire-engine!) and "Red Dragon" (arterial blood!) are favorites of mine, and so is their "Classic Red" (classic - tonally right in between the other two). But they're formulated for fountain pens, so you'll want to mix them with some gum arabic to use with any type of dip pen. And for a spectacular "autumn leaf" flame-red, with gold shimmer that creates golden edges around letters when you use a non-absorbent paper like Tomoegawa - try Pilot Iroshizuku in "Momiji" (also formulated for fountain pens, so beef it up with a little gum arabic).
Hope you find what you're looking for!
--yours, K