As others have said, a lot of how you approach something like this depends on the colours you are using. However, is also depends a lot on HOW you use them.
For instance, Alaitoc is Blue and Yellow. If you use the codex scheme, a blue body with a yellow head, then you have particular limitations which you have to deal with. If you have a yellow undersuit and blue plates, you have a different set of limitations.
For wholesale integration, I find the schemes with the undersuit one colour, and the armoured plates another to be the most versatile. You can maintain a consistent undersuit colour throughout the entire army, without the need to over think things. For instance, my Eldar colours are Red and Green, with a red undersuit and green armour. The red undersuit is present on all my aspect warriors as well, regardless of whether it’s the bone armour of my Banshees, or the black armour of the Dark Reapers.
With the exception of the Fire Dragons (red undersuit and orange plates doesn’t offer much definition) the uniformity prevents the whole ‘taste the rainbow’ effect, while still maintaining the individuality of the different aspects.
That’s not to say that all colours would work as well as Red, however, since it’s rather general and tends to go with just about everything. Aliatoc colours are a little more touchy, in my experience, and may require something of a more deft touch… Have you considered painting a single arm of all your aspect warriors in traditional Craftworld colours? Would painting the weaponry in Alaitoc colours do?
Really, though, as Iri said, you have to try combinations out for yourself and see what works best. I’d recommend doing test schemes of (if you have them) spare Guardians first and see what you can come up with. You clearly want the Aspects to fit with the rest of the army, and not stand out as drastically as GW’s are want to, but only you can decide how much you want them to ‘pop’. And to do that, you have to experiment a little.