Basically. If you are here hoping somebody is going to reveal a shortcut for doing great whites, then I have bad news for you I'm afraid...
Only way is applying a ton of thin coats, and be really patient. That is, if you are going to aply the paints by hand. If you want to duke out the cash for an airbrush, that's about the only way you'll get fast whites (and even then, it's by far the most demanding pigment to get right). But that is what an airbrush does basically: applying really thin coats of paint rather fast. Bad thing is that it's really expensive.
As the old saying goes: Cheap, fast, good. Pick two of those.
But I feel your pain... I have an IG army that uses white as it's primary color. If there is a tip I can give, it's starting from a really light grey color, like vallejo's stonewall grey and then paint thinned white from that point on. It'll still take 5-6 coats to get even coverage of your paint. But at least it'll be shaded.
I started from a dark grey basecoat: like codex grey/cold grey/ etc etc.
Then a very light grey for basecoat, leaving the codex grey in the recesses.
Then 5-6 coats of white.
Judging from your last picture, you'll have to add your shading by hand now. That's doing the work twice. Try the above method once and leave grey in the recesses. Good whites comes down to the shading, as highlighting is no longer an option...
Best of luck with the project.