Balancing Monitor to HPZ3200 printer with Built-in spectrometer

[Jlb]

I have an HPZ3200 printer with a built-in spectrometer and use an HP LP2475w 24" monitor with my MacProQuad. I have a Huey Pro which gives me a supposed screen balance and use paper profiles provided with the various paper types I use. The printer prints beautifully (I have had it for over a year). However, on certain images, there is a red shift and/or density difference between screen and print. I want to upgrade from the Huey Pro to a better color balancing system but am at a loss on how this works with a built-in spectrometer in the printer. Do I take the test print that comes off the printer, then read it with an eyeOne2 or Color Munki? Then how do I transfer that information to make the screen yield the same results. Seems backwards, but don't quite understand the process for the HP printer. Any suggestions or input?
thanks,
Jerry