I haven't used C1 7 yet, but this all looks like my experience with moire with C1 5 and 6. In C1 3x days I used the PhaseOne De-moirize plugin for Photoshop (plugin only worked through CS2 unfortunately, and Phase has never updated it for newer software) Yes, sometimes removing the color moire does leave a luminance moire behind that looks worse. As far as color bleed, sometimes I just have to process one variant of the file with moire correction, then process another without the correction. Then I layer them together in Photoshop using a layer mask to "paint in" the moire correction only where I really need it. I have had to painstakingly clone out luminance moire patterns manually, evening out the "zebra" effect by lightening the dark stripes and darkening the light ones.
I shoot tethered a lot, and whenever I spot moire, I test with the C1 moire tool. If I get luminance moire left behind, I use in-camera techniques - like stopping down a bunch so diffraction softens the details enough to lose the moire, or at least soften the definition enough that no luminance moire is left once the color moire is gone. Sometimes I layer (in Photoshop) a stopped-way-down capture with one at a wider (sharper) aperture, masking in the softer image only where it is really necessary, to take care of the moire.
Moire is a pain, and I cringe when I read people saying it's easy to "just correct in software". Sometimes it is, but often it is not.