2 AM bored listening to The Killers Greatest Hits so I figured I would pop in
Anyway, a dark purple will have blue at full and just a touch of red. The shade of blue LED you have will be the limiting factor in the darkness of the purple (regular or royal). As for a dark pink, that will be a combination of red and blue, most likely more red than blue. So I would start with red all the way up and add blue till you get what you want. If find the hue of purple and/or pink you want but it is a little too dark, add a bit of green in to lighten it up.
As for white and amber LEDs, they only really help in making pastel colors (pale pinks and purples, light lavenders, ambers, and blues) and a 'true' white. The white LED generally helps more than the amber one unless you are looking for a specific orange or amber. Green and red LEDs get to a point which they almost seem to snap from amber to yellow. The amber LED helps with that.
What I generally use LEDs for (backdrops, overhead lighting, back lighting, effect lighting), I generally can't get enough saturation so even fixtures with white and amber LEDs in them, I almost never use them. So I wouldn't be too concerned about not having white and/or amber LEDs, especially since you are looking for high saturation like me.