Paul
You might want to have a look at the printer options in Lightroom. Try selecting a print dpi of 720. Most printers have a natural resolution of around 720 or 1400 dpi. If your machine is similar than keeping the the printing resolution at a multiple of 360 make things easier for the interpolation part of the printing software. Although to be honest I don't think this should really affect the apparent sharpness. The other adjustment to do is set the print sharpening to High. I don't think their is much difference between low and medium, so High should help. You could also try changing the type of paper surface you select. Try Matt and Lustre options. Generally these control the ink laydown. It may be that the Harman paper is being "over inked " If none of these help the I'm afraid I'm out of ideas. You could try contacting Harman direct and see if they've got any sugestions. Alternativly stick with the papers that give you good results.
The problem with generic profiles is just that. They are generic. There will always be some slight variation with them, some will be worse than others. An option would be to have a custom profile made. There are several companies that for a small fee produce them for you. Someone like the imaging warehouse, based just outside Stratford upon Avon offer this. You simply buy a book of vouchers, and they will produce custom profiles for you. There web site is here
http://www.theimagingwarehouse.com/. I've not used them but they seem to do a good job from what I hear. There are probably others who offer the service
The other option , and this depends on the cast you have is to put a small offset into you print output. Now this works provided it's only a small cast, and is overall not limited one part of the image. i.e highlights. With the image on the screen compare it to the print, and adjust the screen to match the print. ( don't save anything) . Now apply an equal but opposite correction. For example if you need ( in Lightroom) a -10 correction on the green/magenta tint control to match the print. change this to a +10 . I'd suggest you do this either using a virtual copy, or preferably to the soft proofed copy.
Ideally getting your printer profiled ( and it's not that expensive) is the ideal way to go, but whilst you are experimenting with papers the colour correction method may be the easiest option
John C