I used to put a lot of work into getting good big prints from my old canon 1D 4.1 Mpix camera and have a few suggestions for you. While the printer drivers might be the best at upresing, you might find some more pleasing results using one of the many programs to upscale digital files.
What algorithm will work best kind of depends on what your image has as its subject. I've found that lanzos (geniune fractals) type routines do best with inorganic objects such as bulidings, boxes and stuff, while spline and other mathematical routines do better with plants, flowers, people. Lanzos will upsize a dot into a square, while s-spline will make a square a circle when it upscales. Circles look more natural to me, but YMMV.
You'll have to pay particular attention to sharpening. I like to do this on masks (and use pixel genius photokit sharpener) You do want to sharpen some things before upresing like certain edges you want to be really defined, and other things not. You kind of have to understand what how the upscale software is going to work, and that takes experience. Sometimes you'll get ugly halos if you sharpen too much in advance and other times you need some before upsizing to get the edges to hold. Again it depends on the subject, and you'll have to sharpen again after upresing, both for edges and again for print output. It takes a lot of work to really make a good print from a small file. Oh yeah, if you have a noisy file you need to run neat image or some other noise removal program to clean up the file. Noise gets amplified in upscaling.
If this seems like a lot of work it is. One thing to consider is lightjet output from a service bureau. The lightjet print engine has a very good upres routine that includes sharpening. I've gotten great results this way without as much effort. I don't have the HP but have tried this with both the epson 7600 and 4000 printers and found that by upresing to 360 dpi using smart algorithms and careful sharpening and noise reduction, I could get a significantly better looking print than just sending 180 dpi.
Anyway good luck!
btw - I have found that I've gotten the best results with PhotoZoom Pro (which used to be S-Spline pro) as it has many different mathematical upres routines.