1. When dying, you really need to consider the dimensions and wall thickness of your object ; the smaller & thinner a part, the more likely it is the dye will impregnate it deeper. Remember that the Strong Flexible materials ( even if Polished ) are a porous material, sort of like brickstone.
Indeed, I use a pyrex roaster for the dye bath - then dip the parts into it with the sifter. Your idea of using a second roaster with boiling water sounds too risky and unstable. I use the stove method, so I can see when the dye boils in the pot, then pour it into the pyrex roaster immediately. If it cools down and I need it to be boiling hot again, I take the parts out and I simply heat the dye up on the stove again.
In my case, the dimensions for some of my parts can be very small, as small as 0.5 square cm. Since these parts are for detailed toys, they contain many small detailings such as ridges, relief sculptings (such as text ). Such outer surface details sticking out a millimeter, will surely be fully dye impregnated. Sanding it down for the hope of finding bare white will most likely be futile.
How deep it impregnates, does indeed depend on the time you keep it submerged in the dye bath as well; but do keep in mind general rule of thumb;
- To attain a dark color, dye time is longer. ( 1 minute or longer)
- To attain a light tone color, dye time must be kept short. ( some times as short as 20 - 30 seconds )
Only you know the extent of variation in wall thickness your objects have, so if you need it to be a dark color it will need to be submerged longer, which in turn means the dye might have gone deeper than surface deep.
With the aesthetic goal you have described, it will probably require some testing to get a feel for the way the dye impregnates different parts of your object - so, I suggest printing some extra test samples.
2. Use a meassuring cup. The Rit Dye bottles usually contain a net 207ML. That's just enough for a small parts dye bath, so I would empty that entire bottle in the meassuring cup and add water until the total reaches about 300 - 350ML. I would suggest that dye to water ratio. This also depends a bit on the strength of the dye. If you want a light tone color, you can raise the water ratio a bit higher to say : 50% dye - 50% water. Remember to shake the dye bottle before you use it because pigment might have shifted and sunk to the bottom of the bottle.
3. Rinsing ; yes, just hold the sifter with the parts under running tapwater. You will visually see how the water 'peels' off the dye which hasn't stuck to the object. ( sometimes it will look really dark while in the dye bath after just 30 seconds already, then take the part out and rinse it, revealing a much lighter tone. - so, it depends on the duration of dye bath )
4. I have not used the colorstay fixative. Many of my toy parts contain balljoints and other kinds of friction areas ; so far I have had NO issues of dye 'rubbing' off, so no need for this fixative stuff. Sounds a bit like a marketing ploy to me - unless they mean it ensures color quality due to the super long term effects of UV sunlight exposure. But even in that respect, I have seen no dye color discoloration yet.
5. Dyes ; I would suggest to start with Rit Dye More where possible. In my case, I needed super light turqoise which I apparently could not achieve with the limited color range of the Rit Dye More line. If that's the case for the shade of lemon/lime you have in mind, you might need to get colors from the Rit Dye Liquid line.
I would suggest starting with Rit Dye More Graphite for black - then rinse and sand it down at the sections you want to reveal white ( again, keep in mind this will depend on wall thickness and dye time. Highly depends on the model ) - then dye it again in your lighter tone color of choice( they might or might not affect the black to limited extent )
6. Last but not least ; Before you start the dye process - ALWAYS, always rinse and clean a WSF(P) object in water and scrub it down with a soft tooth brush first. White powder residu might be stuck in crevices. I once had a case of powder residu and the part came out brilliant deep blue, then some reside powder came out of a little corner crevice and revealed a white spot where I didn't want or expect it to be.
Goodluck !