I knew that I was going to have that same problem when I made mine, so I actually tried batiking. I bought soy wax flakes from Dharma because it's a very flexible wax (which means less crackling) and the melting point is low enough that hot tap water will melt it, so it's approved to go down drains without problems. I then covered my dress form in foil and put on the undyed shirt (you could use pillows or rolls of cloth in plastic, so long as it's the size of your arms and neck) and very very carefully used a paintbrush to apply the wax everywhere that I wanted to stay white. I then dyed the shirt blue with RIT dye and removed the wax! This is what I ended up with:
I still needed a piece of invisible beading elastic to hold the neck closed. It really, really wants to fall down. Since that picture was taken, I've moved the elastic to halfway down instead of only at the top. It replicates the shape better.
This is a more time consuming method, but it allowed the knit to keep all of the stretch without me really having to fuss with getting the trim just so.