Yes the paper choice is critical for problematic reds for sure.
Did I say that for HP's media the highest gamut media is the High Gloss Contract Proofing? It has a higher gloss than the ID Gloss, no HP logo on it, is thinner and less robust, but the white of the paper is better than ID, and the gamut extraordinary. I sent off a copy of the profile to Joseph Holmes and he returned the gamut volume as being higher by far than Epson and still a fair edge higher than Canon both on their respective premium papers. So if you want a paper for colour that has no rival, that should have you getting out the sheets in the sample pack. I have an APS profile of HGProof if you need it.
Off topic . Now that I'm obliged to get back to printing on the 9180, I immediately see the strength in the B&W on the Z. The Z is so neutral, yet brilliant, full of life. The 9180 just doesn't cut it with too much bronzing, coloration. I did cook up a Photoshop curve for printing B&W images via Photoshop handles color, with custom profiles that come closer. Write me if you're interested.