There are a couple insights I can offer that may be helpful. First off I would check what firmware you have. Our printer shipped(we have had it for a while now) with 126.96.36.199. The initial testing with this configuration yielded mixed results. We saw reversals in the blues and found that values below and L* of 40 especially reds lacked saturation compared to the Epson K3. When we upgraded to the latest firmware 188.8.131.52 these problems were fixed.
These two printers have a different gamut. In values below L* 50 the two printers gamut's diverge and you may see the advantage go to the Epson on one image and the HP on the other. In high L* values you will see the HP usually has more gamut. So it's a bit tricky to say one printer has the larger gamut and leave it at that, it really depends on the usable gamut, which of course depends on your image.
Lastly the profile you use, and the means by which you create it, can produce radically different results. The canned profiles are okay. If your reproducing well exposed photographs on a glossy media I think you will find them generally good.
This also holds true for the profiles created using the Easy profile creator. What I have found is that many of the issues you have brought up can be resolved by using a "better" profile. I have three test prints in front of me. One made with the canned profile, one with profiler using the imported numbers read by the on-board spectro, and one from EFI colorproof XF using the Color Manager Package. First, they all look "good". What I do notice are fairly drastic differences in the rendering of the blues, shadow transitions, and low L* saturation in the reds. I also have a print from my Epson 9800 out of Image Print. On the print from the HP using the canned profile the Epson dark saturated red is better, but on the HP image using the Profiler profile the dark saturated red is better on the HP. The APS is still a work in progress, and my initial testing is cautiously optimistic.
Also, as you noticed, the red looks orange and the blue is more of a violet. I've talked to some of the HP engineers and this is by design. The colors by themselves do look a little strange, but it's designed to work in a complimentary manner with the rest of the inks to expand the gamut. So it just a matter of getting the printer to make the best use of the colors it has at it's disposal.
This is a nice piece of hardware. It's brand new and it will take time to figure out the best way to drive it. Think of the difference the Atkinson profiles made to someone using an Epson 7/9600 series printer vs. the canned Epson profiles. That said there are inherent design differences and HP made a choice to target gamut above L* 50. They were shooting for percentages, assuming that on a majority of images there would be a usable gamut increase. I think this is good logic, although as your aware there will be times when this is not an advantage.
I hope this helps somewhat. Please feel free to ping me with any questions. There is also a gamut comparison movie that should be up on our website by now, that illustrates some of the issues I've mentioned. www.spectraflow.com