The best you can hope for is to pick through the base colors and try to come up with the best matches to the pantone base colors in offset inks. then you can use the measurements off the chip to get your base ratio.
It will always come down to your eye and the tested dried ink if you are trying for exact matches. You can mix a color that is bang on and then print it on two different types of paper and have colors that are way off when compared to each other. it's the nature of our inks. they are naturally opaque. pantone colour books are printed offset and naturally transparent.
Same with mixing wet/in the can. it will rarely match exactly to a dried print. print it through 2 different meshes and it can affect it. thin it down and it will be lighter at the start of the run, and darker at the end.
there was a line of plastisol I used - International coatings i think - that had pantone base colors, and I watched a novice (she had only started printing the day before, absolutley no color mixing knowledge) nail a couple of colors just by following the formula and using a scale. I was impressed.
Haven't seen that in WB - not when you are mixing green shade blue and yellow shade red.
use the ratio guide and the list of component colors, but mostly trust your eye, the finger smear, and actual printed testing. And always preface any discussion of a client's colours with - "oh, that colour, that's almost impossible to mix in screenprinting"
then if you let them tell you to darken or lighten a test print (you usually don't have to actually do it) they will agree, "that's perfect!"
Most ink companies will mix PMS colors for you for a fee. I've only used this service a couple times when working with UV, where I've wanted them to spot match and figure out adhesion. I sent them the substrate and let them figure it out.
Remember that WB inks dry darker, so you have to force dry your prints to test the color match. White ink will always kill the chroma, so if you need something light and bright use base and the white of the paper stock. Or if the paper isn't white prime with white.
Very familiar are we with with Red Shade Blue and Blue Shade Red from Unions Plastisol mix system. We almost always have interns do it because its an easy system and pretty accurate. I've run into the same issue with paint when you try to match pantones, difficult because of transparent system vs. opaque.
I wonder if any of Union's ratios would translate with TW's colors.
I'll give it a shot and let you know how it turns out.
I the design industry we call that move the Ceramic dolphin technique.
Give the customer something you know they won't like next to your picks, they get to turn something down and feel like they've contributed.