What you describe is not clear.... most good video cards have two outputs for two monitors, so you don't need two cards to run a 2-monitor workstation.
We run 4-monitor workstations, and have about 30 running this way for medical work. Have been doing this for years with HP workstations from the xw6400 into the Z640 eras, to include xw4600s and Z400s. I have not worked with the Z220, personally.
We don't mix major brands.... only nVidia Quadro cards for this because their ODE drivers have the special grayscale drivers we need for our Dome monitors built in. Here are two combinations that are rock solid: FX1800 for the two side color monitors, and FX3700 for the two central grayscale monitors. Or, a Quadro 2000D for the two central grayscales and a regular Quadro 2000 for the two side color monitors. The two side colors are usually NEC (or Dome) 2MP monitors, and the central grayscales are two Dome 3MP or 5MP monitors.
I make sure both the cards are listed in the nVidia documentation as being approved for the ODE drivers we download, and generally keep our drivers up to date. The "ODE" refers to Optimal Drivers for Enterprise, and are the default drivers you'll get if you go to the nVidia download site for Quadro cards. My Windows Update settings do not allow automatic download and install of updated nVidia drivers.... we need to avoid unpredicted "upgrades".
If you look at the HP QuickSpecs for the Z220 CMT there are very few circumstances that the workstation supports using two cards, and those are all nVidia cards (none for AMD). Also, there is zero support for "mixing" of cards as you are trying to do.
I don't hesitate to buy these nVidia cards off eBay, and the price of experimenting is very reasonable that way. I do use HP nVidia firmware updaters to get the cards to the most recent HP standard, and those updaters also work perfectly on non-HP cards of the same type (such as from Dell, Lenovo).