To answer your questions ... I am using ProPhoto RGB as my working RGB space. I have experimented with both Perceptual and Rel. Col. intents. I have not tried converting to Adobe RGB first before trying the gamut mapping -- I did not know that this might help, but I'll give it a try.
I'm surprised you haven't experimented with 'saturation' intent. There's no doubt this rendering intent delivers more saturated colors. I believe the 2200 is a pigment based printer with a similar gamut to the 7600 which I use. Some time ago I was trying to get a 'wow!' effect in prints I was making of a friend's painted copies of some Van Gogh works (which I'd photographed using my D60). The painter had emphasised the saturation of the primary colors that Van Gogh was fond of and which often look pale and faded in many reproductions of Van Gogh in art books. I was really surprised at just how rich and solid I could get the reds, yellows and blues using saturation intent, especially the blues and yellows, (using the ProPhoto space of course).
Another consideration is the printer profile. I've actually done the following experiment with my 7600, although it can get a bit tedious messing around in this way, and sometimes I seriously wonder if I should be doing something else like getting a life .
I created a pure yellow square in a new document in Photoshop, in the ProPhoto space, ie. 255,255,0. In proof colors, this yellow was way out of gamut. It required a reduction of 11 pts in hue/sat control to get it back in gamut which, interesting or not, resulted in the numbers changing to 241,241,14.
But I ignored the out-of-gamut warning and printed the yellow square on Premium Lustre, once using the Bill Atkinson profile for Prem Lustre and again using the standard Epson profile that ships with the printer.
The difference was staggering. The Atkinson profile produced a rich, solid yellow as yellow as the ink in the cartridge. The Epson profile produced a weak yellow that was almost beige. In fact it didn't even look as yellow as the same 255,255,0 yellow in sRGB which I also printed with the epson profile.