The 85xx DC load I have will not let me set above 3 A in CC mode.

The cause of this could be that the instrument is set to enable range mode, which restricts to a lower range in order to improve accuracy and resolution in measurements within the range.  In the lower range, the measurable and settable current limits to 3 A.  Other models in the series vary depending on their limitations.

The advantages of having lower range enabled is that an extra digit of precision/resolution will be available on display when measuring the inputs. To turn off range mode, go into the menu system from the front panel (shift + 0). Under the "CONFIG" submenu, scroll or use arrow keys to browse through the menu until "RANGE SELECT" is displayed. Set this to "OFF" and press enter to save the changed setting. This will turn off lower range mode. To turn it back on, just select "ON" and press enter to confirm and save the changed setting.